Random math help.. -Hijacked with calculus 3 question

[solipsism]

this whole 'apply the negative' concept doesn't even exist in PEMDAS to begin with.

Except that it does because the exponent is handled before subtraction, you can call it a negative but it is still handled the same way as minus. The picture posted illustrates the difference between (-6)^2 and -6^2.

[solipsism]

you should treat "-6²" like "-(6*6)" is like saying you should treat "34²" as "3(4*4)".

How so? There is no operator symbol between the 3 and the 4 that would dictate the exponent acting on only the 4 and not both the 3 and 4 together, whereas the minus/negative symbol is not a number it is an operator. That's a bad analogy.

[Deadgye]

Except that it does because the exponent is handled before subtraction, you can call it a negative but it is still handled the same way as minus. The picture posted illustrates the difference between (-6)^2 and -6^2.

But it's really not handled the same way as a minus sign, lol. Negative numbers are not privy to order of operations because of the sign they carry, they are a number.

How so? There is no operator symbol between the 3 and the 4 that would dictate the exponent acting on only the 4 and not both the 3 and 4 together, whereas the minus/negative symbol is not a number it is an operator. That's a bad analogy.

It's a perfect analogy. The confusion comes into play because we use the same symbol for displaying negative for a negative number that we do for the subtraction operation. If you use a quality calculator you'll find there are two 'buttons', one for minus and one for negative.

Even windows calculator treats "-4²" as "(-4) * (-4) = 16". You're going to have to enter in "0 - 4²" in order to get -16.

[Ksandra]

Except that it does because the exponent is handled before subtraction, you can call it a negative but it is still handled the same way as minus. The picture posted illustrates the difference between (-6)^2 and -6^2.

Please do not in any way shape or form take this as an insult, but how old are you?

As I said I am honestly curious as to when this came about. Is this something new?

I know I know, I took algebra back in 1992? But I can say with 100% certainty that without a doubt -6^2 would have been solved as 36.

I am not arguing that is still the standard or you are wrong, I am just curious when this changed happened.

[solipsism]

Please do not in any way shape or form take this as an insult, but how old are you?

As I said I am honestly curious as to when this came about. Is this something new?

I know I know, I took algebra back in 1992? But I can say with 100% certainty that without a doubt -6^2 would have been solved as 36.

I am not arguing that is still the standard or you are wrong, I am just curious when this changed happened.

I am 28 and this is exactly how it was taught to me and I have never heard or seen anyone solve something such as -6^2 differently. I don't see how there could be any debate about solving -6^2, if you want to square a negative number you would write it as (-6)^2. I am unaware of there being any change.

[Jefe]

What? -4^2 = -16 and (-4)^2 = 16. Done.

[solipsism]

Even windows calculator treats "-4²" as "(-4) * (-4) = 16". You're going to have to enter in "0 - 4²" in order to get -16.

Did you see the wolfram alpha link that was posted earlier?

And the picture of the emulated TI calculator?

[Ksandra]

I am 28 and this is exactly how it was taught to me and I have never heard or seen anyone solve something such as -6^2 differently. I don't see how there could be any debate about solving -6^2, if you want to square a negative number you would write it as (-6)^2. I am unaware of there being any change.

Equally, I had never ever heard of anyone solving it another way until this thread. lol


28 is a 5 years difference which is definitely enough of a difference for the computer era, so that could be why.

[Deadgye]

Did you see the wolfram alpha link that was posted earlier?

And the picture of the emulated TI calculator?

Broke out my TI calculator and it gives me the results you're saying. Guess this wasn't as one sided as I thought it was. We agree on literally everything except for the representation of "-x^y". When written out I have my argument of spaces for deliminating, and when put into a program with no spaces I have my argument of there being separate symbols. But then some programs treat the negative symbol one way and some programs treat it the other way.

Not really sure whether one is correct and one isn't, or whether it's just fucked.

[Jefe]

^You're wrong.

[Deadgye]

If I was absolutely 100% wrong, then windows calculator would disagree with me too. You can always make the argument that it transforms "x^y" into "function(x)" and therefore that the parenthesis are there I guess.

My stance probably stems from dealing with multiple mathematics systems in which negation has a higher priority than exponentiation.

[solipsism]

If I was absolutely 100% wrong, then windows calculator would disagree with me too. You can always make the argument that it transforms "x^y" into "function(x)" and therefore that the parenthesis are there I guess.

Earlier today TBR linked a couple of KB articles regarding Excel doing the same thing. I don't have links for them but there is this. http://forums.anandtech.com/showthread.php?t=1548657

[Deadgye]

You can see it mentioned in the wiki article on order of operation as well: http://en.wikipedia.org/wiki/Order_o...o_the_standard

In written or printed mathematics, the expression −3² is interpreted to mean −(3²) = −9, but in some applications and programming languages, notably the application Microsoft Office Excel and the programming language bc, unary operators have a higher priority than binary operators, that is, the unary minus (negation) has higher precedence than exponentiation, so in those languages −3² will be interpreted as (−3)² = 9. Note this does not apply to the binary operator −; for example while the formulas =-2^2 and =0+-2^2 return 4 in Microsoft Excel, the formula =0-2^2 returns −4. In cases where there is the possibility that the notation might be misinterpreted, parentheses are usually used to clarify the intended meaning, however due to the syntax of most major programming languages, it is usually hard or impossible to be ambiguous.

[RKenshin]

This is all sounding far more like it's based around how programming languages are interpreting it, than anything else.

Except that it does because the exponent is handled before subtraction, you can call it a negative but it is still handled the same way as minus. The picture posted illustrates the difference between (-6)^2 and -6^2.

It may work fine that way, but definitely isn't the way I was taught. And I haven't seen any definition of PEMDAS that says anything to the line of "apply the negative" at the addition/subtraction point.

This just seems like a lazy way of writing -1*(6^2), if that's ultimately what -6^2 should communicate. It doesn't make sense to me to treat the negative symbol as a separate piece, as if negative numbers don't exist on their own before the PEMD priority of PEMDAS.

But hey, whatever works.

[Yugl]

This is all sounding far more like it's based around how programming languages are interpreting it, than anything else.

It may work fine that way, but definitely isn't the way I was taught. And I haven't seen any definition of PEMDAS that says anything to the line of "apply the negative" at the addition/subtraction point.

This just seems like a lazy way of writing -1*(6^2), if that's ultimately what -6^2 should communicate. It doesn't make sense to me to treat the negative symbol as a separate piece, as if negative numbers don't exist on their own before the PEMD priority of PEMDAS.

But hey, whatever works.

Actually, as the article states, programming languages are more likely to deviate from the norm and agree with your statement (They make up their own rules; that's why many will have a section detailing precedence). As I mentioned previously, you can either take that to mean multiplying by negative one over the entire term or subtraction as Nova pointed out. I'm not sure what you mean by treating the negative symbol as a separate piece, but multiplication and subtraction take care of the unary in such cases. This is also why students new to exponents will see (-6^2) and (-6)^2 problems consecutively; this point is to demonstrate the difference.

[BaneTheBrawler]

But it's really not handled the same way as a minus sign, lol. Negative numbers are not privy to order of operations because of the sign they carry, they are a number.

the way i learned math, this is correct.

[Moss]

I am 28 and this is exactly how it was taught to me and I have never heard or seen anyone solve something such as -6^2 differently. I don't see how there could be any debate about solving -6^2, if you want to square a negative number you would write it as (-6)^2. I am unaware of there being any change.

This is how teachin ladies told it to me.

[Teorem]

Equally, I had never ever heard of anyone solving it another way until this thread. lol

28 is a 5 years difference which is definitely enough of a difference for the computer era, so that could be why.

I'm about the same age as you are (IIRC), took my first algebra class in '90, and read -6^2 as -36.

If you had a single term of -x^2, it was always an implicit -1 * x^2. Otherwise, you'd be able to incorrectly convert any term from -x^2 to x^2 with the additive identity and commutative properties.

Edit: Also, our schools were too poor to believe in technology, so it was not a significant influence. Though I'm pretty sure Number Munchers would have seen it as -36, too.

[Nevermore]

So since there is a math thread on the front page maybe you guys/gals can help me out. I haven't stepped foot in a math class for 6 years now so go easy on me please.

I'm trying to find the equation of a line through (1,-6) parallel to x+2y=6.

I understand the steps I have to take to get the answer just no clue what to do to get the answer if that makes any sense. Getting the equation into y=mx+b form is really what gets me stuck. You subtract the x then get 2y= -x + 6 then you would divide by 2 to get the y alone? Or can it be 2y? After that no matter what I plug into the y-y1=m(x-x1) is wrong and the answer ends up nowhere near what the book says it is.

Any help would be appreciated.

[Marokko]

I've always assumed -6^2 would be treated like -(6^2). This way makes sense to me because then when you're solving an expression like x-6^2 you would get x-36 instead of +. Basically treating all - signs as subtraction until placed inside parentheses.

I'm a math major though, in case that makes my perspective better/worse for a kid's textbook...