-2^2 = ??

[BeerhandBop]

Another Great Internet Debate.

is it 4 or -4 ???

[froshie1]

It's 4.


para maging mahaba ang sinulat.

[valdeaunia]

Why would the answer be -4? :confused:

[math_techie]

diba 4 naman talaga?

[deathbringer07]

alam ko +4..

kasi di ba pag parehas ang sign, positive ang kalalabasan, eh pwede din namang isulat ang -2^2 ng -2*-2. parehas silang negative, kaya positive ang sagot.

[superlanggam]

Another Great Internet Debate.

is it 4 or -4 ???

-2^2 = 4

(-2)(-2) = 4

neg x neg = positive

[yuel0022]

what do you mean by -2^2? -2 raised to 2, tama ba?

kung ganon, 4 ang sagot,diba? :confused:

[neinsager]

you mean (-2)^2? it's 4, not -4.

[Mr. Yo]

Ang hirap naman. :lol:

(-2)^2 = 4
-2^2 = -4

:)

[rational]

Ha ha... Was thinking that this is a really stupid question.... and that it should be -4.
Then, DAMN.... I tried it on Excel and it evaluated it as 4! :rotflmao:

Matlab evaluated it as -4. MuPad evaluated it as -4.

[math_techie]

it depends kung anong order ng operation ang gagamitin mo. some may argue that its 4 kasi it is -2 squared. Others may argue na -4 kasi mas mataas ang precedence ng ^ kesa sa pagmumultiply ng -1.

[la_flash]

it depends kung anong order ng operation ang gagamitin mo. some may argue that its 4 kasi it is -2 squared. Others may argue na -4 kasi mas mataas ang precedence ng ^ kesa sa pagmumultiply ng -1.

I agree.

It's a matter of asking if -2 should be treated as one qty before raising it to the 2nd power, or it should be treated as multiplication of two different quantities --- 2 and -1.

I don't know about you guys, but if -2 should be treated as one qty, then this should be written as (-2)^2, else it will be the same as (-1)(2)^2.


A little bit messy, eh?

[BeerhandBop]

as i've said. it's another great intarwebz math debate.

some argue na it's


-(2^2) = 4

some debate that -2 x -2 = +4

:)

[yuel0022]

I agree.

It's a matter of asking if -2 should be treated as one qty before raising it to the 2nd power, or it should be treated as multiplication of two different quantities --- 2 and -1.

I don't know about you guys, but if -2 should be treated as one qty, then this should be written as (-2)^2, else it will be the same as (-1)(2)^2.


A little bit messy, eh?

agree.

so we should've put parentheses to make things clear.

like:

(-2)^2 = 4

-(2^2) = -4

[math_techie]

-2 is a single quantity...yeah it is the product of -1 and 2. But in the case of -2, the (-) at the left is not an operator, it is not -1, but rather it is an indicator that the number is -2 (the additive inverse of 2).

So since one quantity lang naman ang -2, the only operator in -2^2 is the (^) symbol.

[pink_gold]

+4.....:bungi: my math teacher in HS taught us that any number expressed with a negative sign is always treated as (-n)..else, it should've been expressed as -(n)

[Dacs]

It can be rephrased as this:

How do we evaluate 4 - 2^2?

Can it either be:

1. Zero since 4 - (2^2) = 4 - 4 = 0 or
2. Eight since 4 + (-2^2) = 4 + 4 = 8?

[Dacs]

Placing a negative is a unary operation.

In most programming languages, it takes precedence before exponents.

I think the problem is ambiguous to begin with so, parenthesis must be used to resolve the ambiguity.

[la_flash]

It can be rephrased as this:

How do we evaluate 4 - 2^2?

Can it either be:

1. Zero since 4 - (2^2) = 4 - 4 = 0 or
2. Eight since 4 + (-2^2) = 4 + 4 = 8?

Exactly my point. Use () as much as possible if you want to treat it as one qty.

@math_techie, I don't know but that causes a lot of confusion among students.

[la_flash]

Placing a negative is a unary operation.

In most programming languages, it takes precedence before exponents.

I think the problem is ambiguous to begin with so, parenthesis must be used to resolve the ambiguity.

Wow Dacs. A ChE who knows programming... I'm impressed. :D

[lurkerguy25]

alam ko +4 ang sagot dyan :):)

[skuidward]

I agree with la_flash and Dacs. Depende yan sa grouping symbols.

Pero if we are to base the answer on the given equation by TS, +4 ang sagot ko.

[Dacs]

I've had my share of coding programs :) pasttime ko yan nung nagbubulakbol pa ako nung college :D

Kaya minsan di ko rin maiwasan gumamit ng () para di siya maging ambiguous. I think we all have our share of debugging codes/formulas in excel that is caused by a simple omission of ().

Going back to the topic, I'm afraid the ambiguity stems out of our own biases on how to treat the hierarchy of mathematical operations.

Ang pumapasok agad sa atin pag nakita natin ang -2^2 is negative two squared. But it's just as equally logical to think of it as negative of two squared.

As I said, it all boils down to our biases. IMO nagsimula yan nung itinuturo sa atin for the first time ang exponents. We tend to think of a negative quantity raised to a certain power as a negative quantity first, then we notice the power.

[skuidward]

Yup, I agree with the other posters regarding the placement of grouping symbols.

My answer based on the original equation, +4 ang sagot ko. :D

[tanpearl]

diba depende yun?

-(2)^2 = -4
tapos pag (-2)^2 = 4?

[-jps-]

+4 pa rin yung sagot

-2^2= 4

-(2^2) = -4

[BeerhandBop]

LoLs.


try googling -2^2 and you get -4.

[iRebirth]

Indeed another great internet debate! :lol:

[ubermensch14]

My answer: -2^2 = -4.
Yes, if we'll just look at the way it was written without any other information, it is negative four.

We all agree that -2^2 could confuse people. However, if one really meant (-2)^2 but wrote down -2^2, then this for me is not good notation. So what tipped things over to the -4 side instead of +4 for me? There has got to be only one meaning, since we can't have flexibility in mathematics, where things are very precise. There has to be a widely known standard so that when we look at -2^2, we should all be thinking of the same operations.

This standard is PEMDAS: parentheses, exponents, multiplication, division, addition and subtraction. According to this rule, we square 2 first (exponent), then multiply by -1 (multiplication), giving us -4 in the end.

Next question would be, why is PEMDAS this way? I don't know, but that's the standard.

Naisip ko lang: how would we solve for the value of 10-x^2 if x=2? In other words, what is the value of 10-2^2? Di ba we square two first, then subtract it from 10? Ngayon, what if instead of 10, we had 0? Then we would have 0-2^2. Just like the previous example, if we are to be consistent (and we should), we should square two first before worrying about the preceding negative sign. And since 0-2^2 is the same as -2^2, then we should again square first before even looking at the negative sign.

As someone posted, Matlab and Mathematica (softwares) say it's -4, except for excel. And so I'd like to ask, what were the exact values/formulas specified in excel that gave +4 instead?

[rational]

People, it should be -4. If we had -x^2, would we evaluate it as x^2? Of course not.

Now, the weird thing is the implementation in Excel. Why they did this is beyond me.

@ubermensch: This is what I put into Excel ===> " = -2^2 " (without the quotes of course) and it came out as -4.

[rational]

Man, I just realized how dangerous Excel is.

If you put in "=-2^2", it will give you 4.

If you put in "=1-2^2", it will give you -3.

If you put a "-2" in cell A1 and you put in "-A1^2" in another cell, it will give you 4.

If you put a "-2" in cell A1 and you put in "1-A1^2" in another cell, it will give you -3.

Is that crazy or what?

[la_flash]

Man, I just realized how dangerous Excel is.

If you put in "=-2^2", it will give you 4.

If you put in "=1-2^2", it will give you -3.

If you put a "-2" in cell A1 and you put in "-A1^2" in another cell, it will give you 4.

If you put a "-2" in cell A1 and you put in "1-A1^2" in another cell, it will give you -3.

Is that crazy or what?

There's nothing crazy about that. A1 was squared before you did the other operation.

you should have done cell in A1 = 2 then evaluate -A1^2.. It gave me -4.

[ubermensch]

Man, I just realized how dangerous Excel is.

If you put in "=-2^2", it will give you 4.

If you put in "=1-2^2", it will give you -3.

If you put a "-2" in cell A1 and you put in "-A1^2" in another cell, it will give you 4.

If you put a "-2" in cell A1 and you put in "1-A1^2" in another cell, it will give you -3.

Is that crazy or what?

definitely not rational :lol:

[Dacs]

My answer: -2^2 = -4.
Yes, if we'll just look at the way it was written without any other information, it is negative four.

We all agree that -2^2 could confuse people. However, if one really meant (-2)^2 but wrote down -2^2, then this for me is not good notation. So what tipped things over to the -4 side instead of +4 for me? There has got to be only one meaning, since we can't have flexibility in mathematics, where things are very precise. There has to be a widely known standard so that when we look at -2^2, we should all be thinking of the same operations.

This standard is PEMDAS: parentheses, exponents, multiplication, division, addition and subtraction. According to this rule, we square 2 first (exponent), then multiply by -1 (multiplication), giving us -4 in the end.

Next question would be, why is PEMDAS this way? I don't know, but that's the standard.

Naisip ko lang: how would we solve for the value of 10-x^2 if x=2? In other words, what is the value of 10-2^2? Di ba we square two first, then subtract it from 10? Ngayon, what if instead of 10, we had 0? Then we would have 0-2^2. Just like the previous example, if we are to be consistent (and we should), we should square two first before worrying about the preceding negative sign. And since 0-2^2 is the same as -2^2, then we should again square first before even looking at the negative sign.

As someone posted, Matlab and Mathematica (softwares) say it's -4, except for excel. And so I'd like to ask, what were the exact values/formulas specified in excel that gave +4 instead?
This is problematic for compilers if we don't know the internal workings of program compilation.

As I said, negating a number is a unary operation and in programming, it can be executed in two ways:
1. My C/C++ is quite dull (and correct me if I'm wrong) but I think one can make a, for instance, signed byte a negative number by flipping the most significant bit. For instance: 00000101b is 4d but if we flip the most significant bit into 1 (10000101b) it will become -4d
2. Multiply a value by negative one. For programmers, this will consume processor time and we all know that flipping bits is much faster than multiplying two registers (one is -1 and the other one is the value)

IIRC bit manipulation, such as SHL and SHR, takes precedence before all the other operations, including exponential operations. So if we don't know how the compiler works, this can be problematic in our calculation.

So if we apply this rule, -2^2 will be executed as
1. A unary negative (flip the leftmost bit) and
2. Square the value

This will result in +4.

Any programmers with more experience can comment on this?

And this is unfortunately very significant nowadays since we do almost all our calculations by computers.

[math_techie]

-2 = -1*2, but we have to look at -2 here as a single number in itself and not as a product of -1 and 2. The (-) was placed there as an indicator that -2 is different (and is the additive inverse) of 2. Kasi if we will be looking at numbers as products of other numbers, then we might as well say that 8^2 = 2*4^2 = 32? or 8^2 = 4*2^2 = 16?, so that ^ becomes undefined now.

mathematically, ano ba ang mas naunang concept na nadevelop? yung -2 as an additive inverse or -2 as the product of 2 and -1. I think mas nauna yung -2 as an additive inverse, tapos naging consequential na lang yung pagiging product niya ng 2 and -1.

in the case of variables (example -x^2), the (-) symbols now becomes an operator because we do not know whether x is positive or not, so the (-) symbols tells us that the quantity is the negative of x (whatever x) is, hence the rules on operations takes in effect.

I'll stick to my contention that -2^2 = 4, and -(2^2) would be -4

[rational]

Holy COW!!!

It's even crazier than I thought.

In Excel, if you put in "-2^2", it will give you 4.

BUT, if you put in "0-2^2", it will give you -4!

So basically EXCEL is telling you that 0-2^2 is not equal to -2^2

&#^^!$%$%!!!!!

[-jps-]

LoLs.


try googling -2^2 and you get -4.


4 pa rin

nakalagay sa google ---> -(2^2) = -4 :D

[-jps-]

sige subukan mong -4 sagot mo pag may exam na gnyan

ewan ko lang kung baka batukan ka ng prof mo pag -4 sagot mo

[Dacs]

Holy COW!!!

It's even crazier than I thought.

In Excel, if you put in "-2^2", it will give you 4.

BUT, if you put in "0-2^2", it will give you -4!

So basically EXCEL is telling you that 0-2^2 is not equal to -2^2

&#^^!$%$%!!!!!
It makes sense if you treat the negative as a unary operation.

In the 1st line, the negative is a unary operation, so it takes precedence to the exponent.

In the second line, the negative is actually a subtraction operation (binary operation). Hence, the exponent takes precedence.

[math_techie]

Holy COW!!!

It's even crazier than I thought.

In Excel, if you put in "-2^2", it will give you 4.

BUT, if you put in "0-2^2", it will give you -4!

So basically EXCEL is telling you that 0-2^2 is not equal to -2^2

&#^^!$%$%!!!!!

magkaiba kasi ang gamit ng (-) sa 0-2^2 at sa -2^2, kaya magkaiba ang value nila.

[pink_gold]

sige subukan mong -4 sagot mo pag may exam na gnyan

ewan ko lang kung baka batukan ka ng prof mo pag -4 sagot mo

oo nga..:lol: as if naman na makikipag debate ka pa sa prof mo..impossible na i-consider yang ganyan.. kahit anong number naman ang lagyan mo ng negative sign hindi naman ibig sabihin na -(n)..kaya nga hindi nilagyan ng parentheses kasi understood na yun dapat..

[yuel0022]

It makes sense if you treat the negative as a unary operation.

In the 1st line, the negative is a unary operation, so it takes precedence to the exponent.

In the second line, the negative is actually a subtraction operation (binary operation). Hence, the exponent takes precedence.

I agree.

at sabi nga ni ubermensch, PEMDAS diba.

kung may experience ang tao ng konti sa programming maiintindihan nya to talaga (yung sa excel). pero madali lang naman yan intindihin since PEMDAS nga ang basis *okay*

[I_M_U]

-4 talaga po ang sagot kung i bebase sa math. Nakalilito talaga sa simula pero pagnasanay na, ok lang.

Ito simple analogy.
Pag -x^2 ang expression, di naman natin sinisimplify na x^2 kasi di kasama sa squared ang -1.

[swellbong]

Should be 4. Im positive. :) -2 should be treated as a single number and not a product of -1 and 2. Tama si math techie.

[rational]

magkaiba kasi ang gamit ng (-) sa 0-2^2 at sa -2^2, kaya magkaiba ang value nila.

so, why is the implementation in Excel different from the implementation in Matlab? In Matlab, 0-2^2 is equal to -2^2 as it should be.

Excel algebra is different from Matlab algebra?

[la_flash]

paano ba yan ubermensch, outnumbered tayo. :lol:

Guys, please use parentheses to avoid ambiguity and confusion.

[I_M_U]

-4 talaga kung sa math ibebase. Kasi ang base lang ay 2. Hindi iniinclude ang negative sign pagganun.

+4 lang kung (-2)^2. Tinanong ko pa po teacher ko para po sure.

(Graduating palang po from a science high school kaya fresh pa po sakin and I have already joined philippine math olympiad at MTAP)

[colorado]

-2^2 = 4

2 is a numerical coefficient already.

Unlike sabihin na natin na -x^2. Which is ang numerical coefficient ng -x^2 is 1. Ganito -(1)x^2.

-x^2 = -(1)x^2 = -x^2
-2^2 = 4

negative sign in x pertains to its numerical coefficient 1. unlike doon sa -2^2 na ang negative sign pertains to 2.

----
My answer is +4. :D

[Dacs]

-2 = -1*2, but we have to look at -2 here as a single number in itself and not as a product of -1 and 2. The (-) was placed there as an indicator that -2 is different (and is the additive inverse) of 2. Kasi if we will be looking at numbers as products of other numbers, then we might as well say that 8^2 = 2*4^2 = 32? or 8^2 = 4*2^2 = 16?, so that ^ becomes undefined now.

mathematically, ano ba ang mas naunang concept na nadevelop? yung -2 as an additive inverse or -2 as the product of 2 and -1. I think mas nauna yung -2 as an additive inverse, tapos naging consequential na lang yung pagiging product niya ng 2 and -1.

in the case of variables (example -x^2), the (-) symbols now becomes an operator because we do not know whether x is positive or not, so the (-) symbols tells us that the quantity is the negative of x (whatever x) is, hence the rules on operations takes in effect.

I'll stick to my contention that -2^2 = 4, and -(2^2) would be -4
I agree with this. If we realize that -2 represents a number in the number line (and a consequence of the additive inverse axiom) and not a series of operations (-1 * 2), the ambiguity will be resolved.

[boy_wonder]

Balik tayo sa grade one. :lol:

There's the PEMDAS rule. So exponentiation comes first before subtraction..

In the expression "-2^2", I'm confused with how the "-" sign should be treated. Should it be as a minus sign (operation) or just a negative sign (negation)?

Kasi, I'm thinking na if it's a minus sign (meaning may operation), then there should be a term before "-".. Diba, dapat may minuend at subtrahend sa subtraction? :lol: (Is there any such thing as "implied minuend"? Haha.)

So kung ganun nga, hindi for subtraction ang gamit ng "-". It's just a simple negation, and therefore the expression "-2^2" involves only one operation, which is exponentiation.

4 ang sagot dun. :)

[ubermensch]

This is problematic for compilers if we don't know the internal workings of program compilation.

As I said, negating a number is a unary operation and in programming, it can be executed in two ways:
1. My C/C++ is quite dull (and correct me if I'm wrong) but I think one can make a, for instance, signed byte a negative number by flipping the most significant bit. For instance: 00000101b is 4d but if we flip the most significant bit into 1 (10000101b) it will become -4d
2. Multiply a value by negative one. For programmers, this will consume processor time and we all know that flipping bits is much faster than multiplying two registers (one is -1 and the other one is the value)

IIRC bit manipulation, such as SHL and SHR, takes precedence before all the other operations, including exponential operations. So if we don't know how the compiler works, this can be problematic in our calculation.

So if we apply this rule, -2^2 will be executed as
1. A unary negative (flip the leftmost bit) and
2. Square the value

This will result in +4.

Any programmers with more experience can comment on this?

And this is unfortunately very significant nowadays since we do almost all our calculations by computers.

That is a valid argument. Apparently, may ibang standard sa computer science. Personally, I wish isa lang ang standard. I'm a purist kasi eh, and I know some people who are more hardcore purists than I am.

My friend (a co-teacher before) told me about a student who complained when he got a quiz/exam back. Ang sagot sa isang question kasi ay 0. Eh ang sinulat ng student, a zero with a diagonal bar. Sabi ng student, eh yun ang ginagamit sa computer science (I don't know how the student said it exactly). This student meant to write zero the way he sees it when you type 0 for example sa dos. Eh yung kaibigan ko, ang point niya, sa math naman, that's the empty set. Dapat kasi, we should use the appropriate symbols/notation.

It therefore seems that in deciding what -2^2 is equal to, the answer now depends on whether this is a math statement or a programming statement. As a math person, I'm biased for the mathematical meaning. And according to this meaning, -2^2 is -4.

[ubermensch]

-2 = -1*2, but we have to look at -2 here as a single number in itself and not as a product of -1 and 2. The (-) was placed there as an indicator that -2 is different (and is the additive inverse) of 2. Kasi if we will be looking at numbers as products of other numbers, then we might as well say that 8^2 = 2*4^2 = 32? or 8^2 = 4*2^2 = 16?, so that ^ becomes undefined now.

not necessarily. that's why there is a mathematical standard (pemdas). which then implies that we should consider 8^2 and 2*4^2 as two different things.

mathematically, ano ba ang mas naunang concept na nadevelop? yung -2 as an additive inverse or -2 as the product of 2 and -1. I think mas nauna yung -2 as an additive inverse, tapos naging consequential na lang yung pagiging product niya ng 2 and -1.

I agree. "(-1)(2) = -2" is only a consequence of the definition of -2 as the additive inverse of 2.

If we say that -2^2 is 4 because the negative sign is applied only to the first 2 we're seeing, then what's stopping us from saying instead that the negative sign should be applied to everything that follows it?

in the case of variables (example -x^2), the (-) symbols now becomes an operator because we do not know whether x is positive or not, so the (-) symbols tells us that the quantity is the negative of x (whatever x) is, hence the rules on operations takes in effect.

I'm not sure I understand this part.

I'll stick to my contention that -2^2 = 4, and -(2^2) would be -4

I may not agree with your contention, but I do appreciate posts like we're seeing in this thread over the countless school-bashing posts in The Academe. *okay*

[ubermensch]

Going back to the topic, I'm afraid the ambiguity stems out of our own biases on how to treat the hierarchy of mathematical operations.


That's a nice way of putting it. *okay*

paano ba yan ubermensch, outnumbered tayo. :lol:

Guys, please use parentheses to avoid ambiguity and confusion.

Okay lang kung outnumbered. Basta ba kaya nating paninindigan ang side natin. *okay*

-4 talaga kung sa math ibebase. Kasi ang base lang ay 2. Hindi iniinclude ang negative sign pagganun.

+4 lang kung (-2)^2. Tinanong ko pa po teacher ko para po sure.

(Graduating palang po from a science high school kaya fresh pa po sakin and I have already joined philippine math olympiad at MTAP)

I agree!

[Dacs]

If there's any value that I got from this thread, it's that I now place more parenthesis than usual in my formulas in excel :lol:

May formula ako na ginawa na sa excel just now: (a-b) / - c^2

it means the difference of a and b divided by the negative of c squared

it ended up like this:

=(a-b)/(-(c^2))

Mahirap na ang maging ambiguous :naughty:

[chuboy]

basic math. -4 is the answer anytime of the day.

[la_flash]

We also have discussed this before with my trainor in math. It should be -4 as the expression -2^2 must be read as 2 squared before putting the negative sign.

Also, math should be treated as absolute. There should be only one answer. No ifs and buts.

However, there's a paper questioning the absoluteness of math (na utang pa rin sa akin ng isang tao diyan hehe).

[math_techie]

its on the way we look at -2. If we look at -2 as a number and an operator, then the rules on precedence works, hence -2^2 = -4 if we look at -2 as a single number, then -2^2 is 4.

So perhaps what should be discussed now is whether we consider -2 as a single number and as a number and an operator. I think kasi that -2 is a single number. The (-) symbol merely differentiates it with the number 2.

[rational]

Also, math should be treated as absolute. There should be only one answer. No ifs and buts.



Absolutely agree. (Side note: That's why it's so hard to nego with mathematicians.)

That's why I'm so bothered by the Excel implementation.

[la_flash]

its on the way we look at -2. If we look at -2 as a number and an operator, then the rules on precedence works, hence -2^2 = -4 if we look at -2 as a single number, then -2^2 is 4.

So perhaps what should be discussed now is whether we consider -2 as a single number and as a number and an operator. I think kasi that -2 is a single number. The (-) symbol merely differentiates it with the number 2.

That's where the parentheses comes into play.

-2^2 means that it is the 2 being squared not including the "-".

If we put it as (-2)^2, then that's when this number is treated as a single qty.

[math_techie]

That's where the parentheses comes into play.

-2^2 means that it is the 2 being squared not including the "-".

If we put it as (-2)^2, then that's when this number is treated as a single qty.

pero yun in the absence of the parenthesis, paano natin ngayon siya titingnan?

[la_flash]

pero yun in the absence of the parenthesis, paano natin ngayon siya titingnan?

It is the negative value of 2 squared. That is how I look at it.

[jescythe]

This is problematic for compilers if we don't know the internal workings of program compilation.

As I said, negating a number is a unary operation and in programming, it can be executed in two ways:
1. My C/C++ is quite dull (and correct me if I'm wrong) but I think one can make a, for instance, signed byte a negative number by flipping the most significant bit. For instance: 00000101b is 4d but if we flip the most significant bit into 1 (10000101b) it will become -4d

http://en.wikipedia.org/wiki/Signed_number_representations

most computer architectures use the two's complement in representing numbers since you can easily add or subtract signed numbers straight up. for example assuming 8-bit lang tayo:

5 = 0000 0101b
-3 = 1111 1101b (sa two's complement flip every bit then add 1)

so that
5 + (-3) = 0000 0101b + 1111 1101b = 0000 0010 = 2 (1+1 is 0 carry 1 at yung ignore na yung carry ng leftmost bit addition)


2. Multiply a value by negative one. For programmers, this will consume processor time and we all know that flipping bits is much faster than multiplying two registers (one is -1 and the other one is the value)

IIRC bit manipulation, such as SHL and SHR, takes precedence before all the other operations, including exponential operations. So if we don't know how the compiler works, this can be problematic in our calculation.

So if we apply this rule, -2^2 will be executed as
1. A unary negative (flip the leftmost bit) and
2. Square the value

This will result in +4.

Any programmers with more experience can comment on this?

And this is unfortunately very significant nowadays since we do almost all our calculations by computers.

http://en.wikipedia.org/wiki/Operator_precedence_in_C

multiplication/division (* and /)takes precedence over addition/subtraction (+ and -), which in turn takes precedence over bitwise operation (<< and >>)

and there is no such thing as exponential operator in C. it is actual the function pow() defined in math.h (http://www.opengroup.org/onlinepubs/007908775/xsh/pow.html). the operator ^ is bit-wise exculsive-OR in C.

since we cannot simply write -2^2 in C/C++ (i don't know in other programming languages), i think we cannot use the computer programmers point of view that that equation equals to 4. besides if we are going to use the pow function, then magiging mas malinaw yung meaning ng negative sign i.e. pow(-2,2) ba o -pow(2,2)

[anima9]

google has answered this already

http://www.google.com.ph/search?rlz=1C1CHMG_enPH291PH303&sourceid=chrome&ie=UTF-8&q=-2^2+%3D

[JhunX]

^

Google's answer is -4. Its obvious because Google rewrites the equation as -(2^2)

My first answer is 4.

[-jps-]

yung mga di nagpapractice sa pagsolve ng math problems

ang magsasabing -2^2 = -4. :)

kung nagdududa ka kung bakit hindi -4 ang sagot sa -2^2,

try mo magpractice magsolve ng madaming math problems

at ng maliwanagan ka na +4 ang sagot dyan :D

[the_misfit]

yung mga di nagpapractice sa pagsolve ng math problems

ang magsasabing -2^2 = -4. :)

kung nagdududa ka kung bakit hindi -4 ang sagot sa -2^2,

try mo magpractice magsolve ng madaming math problems

at ng maliwanagan ka na +4 ang sagot dyan :D

ako, nagpapractice sa pagsolve ng math problems pero ang sagot ko ay -4. hindi considered na kasama ng 2 ang (-). makakakuha lang ng +4 kung ang -2 ay enclosed i.e. (-2)^2.

[jescythe]

interesting bit: if we treat ^ operator as exclusive-OR

-2 ^ 2 = 1111 1110 ^ 0000 0010 = 1111 1100 = -4 :D

[ubermensch]

yung mga di nagpapractice sa pagsolve ng math problems

ang magsasabing -2^2 = -4. :)

kung nagdududa ka kung bakit hindi -4 ang sagot sa -2^2,

try mo magpractice magsolve ng madaming math problems

at ng maliwanagan ka na +4 ang sagot dyan :D

ah, sir. :rotflmao:
with all due respect, i've had enough practice. :lol:

[math_techie]

ako, nagpapractice sa pagsolve ng math problems pero ang sagot ko ay -4. hindi considered na kasama ng 2 ang (-). makakakuha lang ng +4 kung ang -2 ay enclosed i.e. (-2)^2.

bakit hindi kasama 2 yung (-)? There is such a number naman ah?

[la_flash]

yung mga di nagpapractice sa pagsolve ng math problems

ang magsasabing -2^2 = -4. :)

kung nagdududa ka kung bakit hindi -4 ang sagot sa -2^2,

try mo magpractice magsolve ng madaming math problems

at ng maliwanagan ka na +4 ang sagot dyan :D

ako din po, maraming practice sa math. pero -4 ang sagot ko ... :D

========================

[Dacs]

jescythe: Thanks for clearing the negative part in programming.

Anyways, it seems the majority of us are still having some confusion on how to treat a negative number. I'm having the impression that most of us think of a negative number as a product of a positive number and negative 1.

But if we start to consider that a negative number is a unique number (and just as real as its positive twin) and not just a product of multiplying -1 with its positive counterpart, then I think we can start to appreciate why -2^2 = 4

[la_flash]

jescythe: Thanks for clearing the negative part in programming.

Anyways, it seems the majority of us are still having some confusion on how to treat a negative number. I'm having the impression that most of us think of a negative number as a product of a positive number and negative 1.

But if we start to consider that a negative number is a unique number (and just as real as its positive twin) and not just a product of multiplying -1 with its positive counterpart, then I think we can start to appreciate why -2^2 = 4

No question that -2 is a unique number.

However, it's a problem of whether it's -2 that is being squared or is it 2 squared first before considering the negative sign.

In other words, in the expression -2^2, is -2 treated a single quantity or not?

[BeerhandBop]

"Guys, please use parentheses to avoid ambiguity and confusion."

the lack of parenthesis actually makes it clear that one 2 is being squared and not -2.

:)


-4 is the answer.

[bamboo_shoot]

bakit hindi kasama 2 yung (-)? There is such a number naman ah?

ah, i mean sa operation. kailangan i-enclose 'yung 2 at (-) if raised to 2 para makuha ang +4. hindi ba ieenclose ang integer kapag iraraise sa power? otherwise, i.e. not enclosed, treat the coefficient independently from its sign. tama ba? :confused:

please correct me if i'm wrong.

[the_misfit]

ah, i mean sa operation. kailangan i-enclose 'yung 2 at (-) if raised to 2 para makuha ang +4. hindi ba ieenclose ang integer kapag iraraise sa power? otherwise, i.e. not enclosed, treat the coefficient independently from its sign. tama ba? :confused:

please correct me if i'm wrong.

ganito lang din dahilan ko.

[Tom Cruz]

negative :)

[math_techie]

let's try 2^-2. In the absence of a paranthesis, ano dapat ang value nito?

is 2^-2 = 2^(-2)? or is this equal to (2^-1)*2? Excel and matlab have the same answer for this expression. They considered -2 as one quantity, and thus the result is 2^-2 = 2^(-2).

[Mr. Yo]

math_techie, maybe you meant (2^-1)^2 and not (2^-1)*2... Bakit may times 2? :confused:

Basta, -2^2 = -4. Kung gusto mong isama yung negative sa pag-square, maglagay ng parenthesis na parang ganito: (-2)^2. Yan ang turo ni teacher. :D Para kasing pag binasa ang -2^2, "the negative of 2 squared" tapos yung (-2)^2, "the square of negative two". So tama, use parentheses to avoid confusion. Ganun na lang. :lol:

[la_flash]

That's entirely different, math_techie.

Exponents are usually superscript, hence it can be easily seen that -2 there is the
exponent of 2.

[fernando_hierro]

yung mga kumuha ng Math 131 dyan
Elementary Set Theory
-2^2 can be 1, -1, 2, -2, etc
it depends on the rule you set for the elements of the set
so for purists, pwede -4 or 4

[parkingboy]

let me dumb down the topic. if 4 is the answer, does that mean that the square root of 4 can have an answer of -2? two negatives multiplied becomes a positive, right?

[fernando_hierro]

yung mga naka pag Math 131
Elementary Set Theory
the answer can be -1, 1, 2, -2 etc
it depends on the rule you set for the elements of the set

[la_flash]

yung mga kumuha ng Math 131 dyan
Elementary Set Theory
-2^2 can be 1, -1, 2, -2, etc
it depends on the rule you set for the elements of the set
so for purists, pwede -4 or 4

I don't think I understood your post.

Could you please elaborate?

[boy_wonder]

let me dumb down the topic. if 4 is the answer, does that mean that the square root of 4 can have an answer of -2? two negatives multiplied becomes a positive, right?

What I know is, any positive real number has two distinct roots: a positive and a negative..



Na-resolve ba how many operations are there in the expression, "-2^2" as it is?

Methinks there's only one, and that's the exponentiation of -2 to the power of two. 4 would be the answer.

If we manipulate kasi, saka lang 'yan magiging ganito:
-1(2)^2 (although this has the same value)
or
-1(2^2) (equal to -4)

Or try expressing "-2^2" in literal terms.. "the negative value of the second power of two"?? Parang pina-complicate eh.. Mas okey ang "negative two raised to two". :D

[the_misfit]

let's try 2^-2. In the absence of a paranthesis, ano dapat ang value nito?

is 2^-2 = 2^(-2)? or is this equal to (2^-1)*2? Excel and matlab have the same answer for this expression. They considered -2 as one quantity, and thus the result is 2^-2 = 2^(-2).

are you trying to prove something? that's entirely a different story eh. pero pareho naman kami ng sagot ng excel at matlab.

[the_misfit]

let me dumb down the topic. if 4 is the answer, does that mean that the square root of 4 can have an answer of -2? two negatives multiplied becomes a positive, right?

square root of 4 equals +/- 2. yes, the square root of 4 can have an answer of -2.

[I_M_U]

Complicated it may seem, yun yung tamang sagot.

[iRebirth]

I wonder what a 5th grader from Japan would think about this thread. :lol:

[sanpo]

(-2 * -2) = 4
- (2*2) = -4 even -1 (2*2) = -4

simple as that. :)

[Ringgold]

(-2 * -2) = 4
- (2*2) = -4 even -1 (2*2) = -4

simple as that. :)

Yeah we know that but what exactly the answer of -2^2?

[maxwelledison]

square root of 4 equals +/- 2. yes, the square root of 4 can have an answer of -2.

If I'm not mistaken, solving x^2 = 4 is different from solving x=√4

The former only asks for values which could satisfy the equation so the answer is +/- 2. For the latter, the answer should be +2 since √4, according to the standards, stands for the positive square root of 4. For the negative answer, the equation should be x = -√4.

[la_flash]

If I'm not mistaken, solving x^2 = 4 is different from solving x=√4

The former only asks for values which could satisfy the equation so the answer is +/- 2. For the latter, the answer should be +2 since √4, according to the standards, stands for the positive square root of 4. For the negative answer, the equation should be x = -√4.

x^2 = 4 is the same x = sqrt (4).

The answers should be the same.

[BeerhandBop]

"let me dumb down the topic. if 4 is the answer, does that mean that the square root of 4 can have an answer of -2? two negatives multiplied becomes a positive, right?"


lol. this is probably the most failure answer i've ever seen for this question.

[Dacs]

From what I've read, I think we all are in agreement on the math.

But what we're debating is on how to interpret the expression.

And I don't think we can settle that since we all have our biases.

Anyways, I'm just dropping by :D

[Juntrix]

Whoa... I'm no mathematician but it's just a bit scary that different software platforms have different interpretations to a single math problem.

In the accounting world, I guess the answer to -2^2 is -4.

Rationale: Conservatism. :lol:

[boy_wonder]

Hey, the problem we have is rather logical than arithmetic. Of course, we all? know that (-2)^2 is 4 and that -(2^2) is -4. :rolleyes:

However, we're given the expression "-2^2". How we are supposed to interpret that is the major business.. And HOW then?

-2^2 =?= (-2)^2
or
-2^2 =?= -(2^2)

My take:
We see that the placing of the parentheses is what subjects the original expression into two different interpretations. Considering the absence of these grouping symbols, what are we gonna do with the negative sign?

Normally, a "-" would give the negative value of the number (or group of operative numbers) it precedes. Since no grouping symbol (and therefore no grouping operation) was included, we just apply the negative to the first "2". Hence, -(2)^2, equal to (-2)^2. And 4 it is..

We can't assume "2^2" as a grouped expression being negated by "-", anyway, or can't we? :confused:

[ubermensch]

If I'm not mistaken, solving x^2 = 4 is different from solving x=√4

The former only asks for values which could satisfy the equation so the answer is +/- 2. For the latter, the answer should be +2 since √4, according to the standards, stands for the positive square root of 4. For the negative answer, the equation should be x = -√4.

I agree. By writing x=√4, we are considering only the principal square root (the nonnegative one). On the other hand, x^2 = 4 as an equation still admits both the positive and negative square roots.

Hey, the problem we have is rather logical than arithmetic. Of course, we all? know that (-2)^2 is 4 and that -(2^2) is -4. :rolleyes:

However, we're given the expression "-2^2". How we are supposed to interpret that is the major business.. And HOW then?

-2^2 =?= (-2)^2
or
-2^2 =?= -(2^2)

My take:
We see that the placing of the parentheses is what subjects the original expression into two different interpretations. Considering the absence of these grouping symbols, what are we gonna do with the negative sign?

Normally, a "-" would give the negative value of the number (or group of operative numbers) it precedes. Since no grouping symbol (and therefore no grouping operation) was included, we just apply the negative to the first "2". Hence, -(2)^2, equal to (-2)^2. And 4 it is..

We can't assume "2^2" as a grouped expression being negated by "-", anyway, or can't we? :confused:

We can. Order of operations. Without any grouping symbol, 2^2 would have to be taken first as the innermost entity (2^2 is grouped implicitly), before we can even look at the negative sign (which is interpreted as subtraction, and so is preceded by exponentiation in the hierarchy). I asked all my officemates (we're all math graduate students) and we are unanimous in our answer: it's -4. Our reasons are all the same - the order of operations.

Without the PEMDAS standard, -2^2 is not well-defined. But with this standard, it should not be ambiguous anymore. Math does not allow for flexible interpretations for a case such as this. There is always some standard that needs to be followed.

[math_techie]

Hey, the problem we have is rather logical than arithmetic. Of course, we all? know that (-2)^2 is 4 and that -(2^2) is -4. :rolleyes:

However, we're given the expression "-2^2". How we are supposed to interpret that is the major business.. And HOW then?

-2^2 =?= (-2)^2
or
-2^2 =?= -(2^2)

My take:
We see that the placing of the parentheses is what subjects the original expression into two different interpretations. Considering the absence of these grouping symbols, what are we gonna do with the negative sign?

Normally, a "-" would give the negative value of the number (or group of operative numbers) it precedes. Since no grouping symbol (and therefore no grouping operation) was included, we just apply the negative to the first "2". Hence, -(2)^2, equal to (-2)^2. And 4 it is..

We can't assume "2^2" as a grouped expression being negated by "-", anyway, or can't we? :confused:

though I agree that 4 is the answer, I disagree with your reason. If you take "-" as an operator that gives the negative value of a number, then it has less precedence than the ^ operator. Hence, the ^ operator must be evaluated first before the "-" operator.

[la_flash]

I agree. By writing x=√4, we are considering only the principal square root (the nonnegative one). On the other hand, x^2 = 4 as an equation still admits both the positive and negative square roots.




hi ubermensch, we differ on this one. They are one and the same. Why consider the principal square root on the first one?

[I_M_U]

Another way to convince you:

Ito proof na talaga.

Look at this expression:
-2^2+0

By commutative property
0-2^2

Use pEmdaS, Exponent first before Subtraction
0-4

It is -4



Pag may nagsabi pa ng +4, ewan ko na lang.

And also consider this monomial sa basic algebra:
-x^2

Hindi naman ito sinisimplify na
x^2
kc hindi naman kasama ang negative sa square eh.

[ubermensch]

hi ubermensch, we differ on this one. They are one and the same. Why consider the principal square root on the first one?

hello la_flash. dun kasi sa una, by the way it was written (kasi ginamit ang square root symbol), implied na principal square root ang tinutukoy.

Check mo yung paragraph after equation (1) dito: http://mathworld.wolfram.com/SquareRoot.html *okay*

[la_flash]

hello la_flash. dun kasi sa una, by the way it was written (kasi ginamit ang square root symbol), implied na principal square root ang tinutukoy.

Check mo yung paragraph after equation (1) dito: http://mathworld.wolfram.com/SquareRoot.html *okay*

ok ubermensch. i think i know now the rationale behind it.

in my mind kasi eh, if it is square root, there must be two possible roots (one positive and one is negative). :lol:

[rational]

I think that all those who really know math agree that it should be -4.

Here's what I'm wondering about now. How do we raise the issue with Microsoft? Very scary that Excel evaluates -2^2 as 4 and then evaluates 0-2^2 as -4.

[math_techie]

Another way to convince you:

Ito proof na talaga.

Look at this expression:
-2^2+0

By commutative property
0-2^2

Use pEmdaS, Exponent first before Subtraction
0-4

It is -4



Pag may nagsabi pa ng +4, ewan ko na lang.


if you really want to use the commutative law here, we'll have:

a+b = b+a
letting a = -2^2 and b = 0, then actually wala ka paring ma proprove kasi we are still left with the same question of finding the value of a. Kasi
a+b ==> (-2^2) + 0 and b+a = 0 + (-2^2). If you believe that -2^2 = 4, then 4+0 = 0+4, similarly, if you believe (-2^2)= -4, then tama ka pa rin -4+0 = 0+(-4).


And also consider this monomial sa basic algebra:
-x^2
Hindi naman ito sinisimplify na
x^2
kc hindi naman kasama ang negative sa square eh.


this is a different case naman. if we use a variable you are enclosing it it a whole number. Hence yung (-) sa -x is an operator telling you that the number is the negative of x (you are operating on x), so the pemdas precedence follows.

This is different in the example, because I claim that the (-) in -2 is not an operator, but rather an indicator. It tells us what the number is kasi if you look at -2, you look at it as a single number and not as a product of -1 and 2. Hence, since -2 is a single number, then walang question sa precedence, kasi isang operator lang naman ang nagaact dun sa -2^2, yung ^ lang..

[I_M_U]

Haha... Bahala na kayo dian. Di na ako magrereply. Basta, -4 ang sagot ko at teacher ko.

[math_techie]

Haha... Bahala na kayo dian. Di na ako magrereply. Basta, -4 ang sagot ko at teacher ko.

yep, PEX is not for the faint hearted. :)

[ubermensch]

ok ubermensch. i think i know now the rationale behind it.

in my mind kasi eh, if it is square root, there must be two possible roots (one positive and one is negative). :lol:

and we learned something new today *okay*

ako rin kasi, i learned something new, mga two years ago, haha. we know that x^2=9 admits 3 and -3 as roots. no question about that. dati, ang akala ko, x=9^{1/2} admits 3 and -3 as roots as well. pero ang standard pala, just like the square root symbol, x=9^{1/2} admits the principal square root only (x=3 only). :lol:

re: math_techie's post (#104): while i agree with I_M_U that the answer is -4, i agree with math_techie that the -4 answer was not defended by the commutative law statements mentioned.

[string-er]

-2^2 = -4
(-2)^2 = 4

[Ringgold]

-2^2 = -4
(-2)^2 = 4

:rolleyes:
-2^2=?
:rolleyes:

[pinoyagent]

it's -4.....

y?

try it in a calculator then you'll know...

another explanation...

-2^2 is like -(2)^2...therefore the answer is -4....

however....(-2)^2 is equal to positive 4......

the answer for this problem is whether the -2 is enclosed or not in a parenthesis

[boy_wonder]

though I agree that 4 is the answer, I disagree with your reason. If you take "-" as an operator that gives the negative value of a number, then it has less precedence than the ^ operator. Hence, the ^ operator must be evaluated first before the "-" operator.

Sorry, but can "-" be considered as an operator (subtraction) in the expression "-2^2"??

As I've said, if it's taken as a minus sign, then there should be a minuend and a subtrahend. Can you point out these two elements of subtraction in "-2^2"? ..Unless there's some sort of implied minuend/subtrahend... How about in "-4", is there really an operation? The "-" as operator?? :confused:


On second thought, why would we need to refer to the PEMDAS rule? I really think there's only one operation involved here.. exponentiation..

[boy_wonder]

I think that all those who really know math agree that it should be -4.

Here's what I'm wondering about now. How do we raise the issue with Microsoft? Very scary that Excel evaluates -2^2 as 4 and then evaluates 0-2^2 as -4.

Tingin ko lang..

Kasi 'yung "-" sa "-2^2" is taken as a sign that gives the negative value of 2, giving us "-2" as one numerical figure. And only one operation is involved, "^" -- exponentiation..

Dun sa "0-2^2", there are two operations: subtraction at multiplication. And three numbers: 0, 2 and another 2.. This is where we can use PEMDAS na.


Well, not scary. Hehe..

[Katchatore]

Sa order of operations (MDAS or whatever), nauuna palagi ang exponential operations bago ang multiplication. A negative sign is basically multiplication of a number to -1.

-4 ang sagot ko.

[math_techie]

Sorry, but can "-" be considered as an operator (subtraction) in the expression "-2^2"??

As I've said, if it's taken as a minus sign, then there should be a minuend and a subtrahend. Can you point out these two elements of subtraction in "-2^2"? ..Unless there's some sort of implied minuend/subtrahend... How about in "-4", is there really an operation? The "-" as operator?? :confused:


On second thought, why would we need to refer to the PEMDAS rule? I really think there's only one operation involved here.. exponentiation..

actually, the "-" symbol can be an operator, that is not subraction. putting a "-" can also mean multiplying -1, so yun, operator din siya.
example, in -x, the "-" symbol acts as an operator that multiply any value of x with -1

[rational]

Thanks for replying. There could be a good reason why microsoft decided to implement that way but what scares me is that every other software I've tried implements -2^2 as -4. The opposite of Excel.

ANy of you have OpenOffice? Would be interesting to see...

[math_techie]

open office says that its 4

[ubermensch]

Tingin ko lang..

Kasi 'yung "-" sa "-2^2" is taken as a sign that gives the negative value of 2, giving us "-2" as one numerical figure. And only one operation is involved, "^" -- exponentiation..

Dun sa "0-2^2", there are two operations: subtraction at multiplication. And three numbers: 0, 2 and another 2.. This is where we can use PEMDAS na.



Here's what I think. The negative sign counts for something. It negates something. Some people think that what it negates is the first 2 (the base 2, as opposed to the exponent 2). However, what's stopping us from thinking that it's everything else that follows that it negates (i.e., the negative sign is negating 2^2=4)? My answer to this question: nothing. Without any standard, we can't really decide whether that negative sign is negating the base 2, or the whole expression 2^2. So whether you look at the negative sign as (a) multiplication by -1, or (b) implied subtraction, we're still back to square one.

-2^2 and 0-2^2 have to be the same. If 0-7=-7, then 0-2^2=-2^2 as well. We can't be inconsistent here. Or at least, the standards can't be inconsistent. This then leaves no room for personal interpretations.

I asked my housemate, who's also a Math graduate student. I hate that he leaves the kitchen sink a mess most of the time, but we both agree that it's -4. *okay*

Thanks for replying. There could be a good reason why microsoft decided to implement that way but what scares me is that every other software I've tried implements -2^2 as -4. The opposite of Excel.

ANy of you have OpenOffice? Would be interesting to see...

I know you already tried Matlab and Mathematica, but I tried them anyway out of curiosity. Yes, -2^2=-4.

I don't have OpenOffice. I did try it though with StarOffice (Spreadsheet) in my office desktop. Just like Excel, the answer it gave was 4. :(

[math_techie]

i don't think we can use the argument 0 - x = - x in this case, because we might be encountering a circular proof here.

we want to prove that : 0-2^2 = -2^2
so what we do is

0 - 2^2 = 0 ==> 0 + (- (2^2)) (since 0 - x ==> 0 + (-x))

from this step, we cannot directly go to the conclusion that 0 - 2^2 = -2^2, unless we show that -(2^2) = -2^2. We are again back to what we initially want to show.

[BeerhandBop]

really. this isn't the same as 1 == 0.99999999999999999 argument where there's argument from both sides.

-2^2 = - 4 is the correct answer. and that's that.

i can't believe this stretched to 3 pages long na.

[ubermensch]

i don't think we can use the argument 0 - x = - x in this case, because we might be encountering a circular proof here.

we want to prove that : 0-2^2 = -2^2
so what we do is

0 - 2^2 = 0 ==> 0 + (- (2^2)) (since 0 - x ==> 0 + (-x))

from this step, we cannot directly go to the conclusion that 0 - 2^2 = -2^2, unless we show that -(2^2) = -2^2. We are again back to what we initially want to show.

Hi math_techie!

The statement 0-2^2=-2^2 is not meant to be proved. I stated it, coming from the point of view that the left-hand side and right-hand side are actually the same. I wanted to mention this, because for some people, it is clear that 0-2^2 is -4, but for some people, -2^2 could actually be +4. But they are the same (0-2^2 and -2^2). I see no reason why they should be different.

I'm not using this as main proof for -2^2=-4. I'm merely appealing to this as something that supports my stand that -2^2=-4. *okay*

[ubermensch]

really. this isn't the same as 1 == 0.99999999999999999 argument where there's argument from both sides.

-2^2 = - 4 is the correct answer. and that's that.

i can't believe this stretched to 3 pages long na.

correction sir. 6 pages na. and because of the post lag, this might actually appear on page 7. :rotflmao:

[math_techie]

Hi math_techie!

The statement 0-2^2=-2^2 is not meant to be proved. I stated it, coming from the point of view that the left-hand side and right-hand side are actually the same. I wanted to mention this, because for some people, it is clear that 0-2^2 is -4, but for some people, -2^2 could actually be +4. But they are the same (0-2^2 and -2^2). I see no reason why they should be different.

I'm not using this as main proof for -2^2=-4. I'm merely appealing to this as something that supports my stand that -2^2=-4. *okay*

hello,

from the way I see it, you are using the fact that -2^2 = 0-2^2 to prove that -2^2 = -(2^2). Tama ba?

kasi from what I see, -2^2 = 0 - 2^2 is not a straightforward fact.

[BeerhandBop]

"correction sir. 6 pages na. and because of the post lag, this might actually appear on page 7. "

40 posts per page in mine. lol.

[swimbod21]

ganito yan...

-2^2 = -4
(-2)^2 = 4
-(2)^2 = -4

[ulymar]

in programming view:

visual basic
(-2) ^ 2 = 4
-2 ^ 2 = -4
-(2 ^ 2) = -4

delphi:

-(round(power(2,2))) = -4
round(power(-2,2)) = 4


br

[boy_wonder]

actually, the "-" symbol can be an operator, that is not subraction. putting a "-" can also mean multiplying -1, so yun, operator din siya.
example, in -x, the "-" symbol acts as an operator that multiply any value of x with -1

Sir, di ba natin pwedeng i-interpret na lang ang "-x" as the simplest form of the number itself? Of course, we can say na -x is -1 times x. But just the same, it's equal to 1 times -x. Pwede rin namang 2x times -(1/2), etc.. My point is, why the need to get the factors the number, or interpret it as a result of some operation?

Saka I think, if ever -1 would actually be multiplied to the number it precedes (or 2 in this case), gagamitan ng parentheses 'yan.. -(2)^2.. That's when we should do multiplication. Kasi we don't assume how a number/numbers in an expression is/are derived, but rather just employ the operations involved.

[math_techie]

hi boy_wonder,

My contention actually is that the (-) in -2^2 is not an operator, but rather it is really part of the number.