Why does BIDMAS not always apply to squaring negative numbers?

[1MileCrash]

The thread is http://https://www.physicsforums.com/showthread.php?p=4626547#post4626547.

If you look at the Youtube video attached, and look at the 'about' info section, it links to a second proof. If you click on that and skip to around the 3:52 mark and listen for 20 seconds, he says that -1²=1, now he used no parentheses so strictly speaking, using BIDMAS, we should do the indices first, so 1² which is obviously 1, and then we should add the negative sign. So if $\chi$=-1, then $\chi$² should equal -1, and 3$\chi$² should be -3 right? He said that 3$\chi$² was +3. Is he wrong?

Sorry to keep this going but I saw it and got confused because he's supposed to be some super duper clever dude, but I thought that he was wrong. It's probably me that's wrong haha, but could someone please just check this. Thanks.

I just watch the video, and he did not say that $-1^{2} = 1$.

If $x=-1$ then he is correct, $x^{2} = 1$, why do you think it should be $-1$? That is x squared, x is negative one, negative one squared is positive one. We've already explained that a negative number squared is positive. x is a negative number. Square it. It is positive.

 

[AlfieD]

I just watch the video, and he did not say that $-1^{2} = 1$.

If $x=-1$ then he is correct, $x^{2} = 1$, why do you think it should be $-1$? That is x squared, x is negative one, negative one squared is positive one. We've already explained that a negative number squared is positive. x is a negative number. Square it. It is positive.

But if you substitute $x$ for it's value of -1, so $x$² would become -1², which would be -1. Or does it not go to that when you change it?

 

[1MileCrash]

But if you substitute $x$ for it's value of -1, so $x$² would become -1², which would be -1. Or does it not go to that when you change it?

No, if you substitute x for its value of -1, it becomes $(-1)^{2}$. You have to preserve the meaning, $-1^{2}$ is in no way, shape, or form, squaring x.

x is -1. Squaring x is squaring -1. Squaring -1 is (-1)^2.

If I wanted to replace the 5 in $5^{2}$ with 2 + 3, would I write $2 + 3^{2}$? No, that is nonsense, they are two different things.

 

[AlfieD]

If I wanted to replace the 5 in $5^{2}$ with 2 + 3, would I write $2 + 3^{2}$? No, that is nonsense.

Yeah, haha that's complete nonsense. Thanks, that was clear. :) I'm pretty sure I'm OK with all of this negative squaring business now. :D

 

[1MileCrash]

Yeah, haha that's complete nonsense. Thanks, that was clear. :) I'm pretty sure I'm OK with all of this negative squaring business now. :D

Furthermore, in general, if you have an equation with some "x", when you put a value in it, you should always put parenthesis around it, because otherwise you can lose any meaning of x if x itself contains operations.

For example, if I have $2x + x^{2}$ and I want to replace x with "y + z," the way to do that is to write $2(y + z) + (y + z)^{2}$. If I don't put those parenthesis for the first term, I am not doubling x, or y + z, I am doubling y and then adding z afterwards, and a similar problem arises for the second term.

 

[AlfieD]

Furthermore, in general, if you have an equation with some "x", when you put a value in it, you should always put parenthesis around it, because otherwise you can lose any meaning of x if x itself contains operations.

For example, if I have $2x + x^{2}$ and I want to replace x with "y + z," the way to do that is to write $2(y + z) + (y + z)^{2}$. If I don't put those parenthesis for the first term, I am not doubling x, or y + z, I am doubling y and then adding z afterwards, and a similar problem arises for the second term.

Yeah, awesome, I understand that.

 

[Borek]

But if you substitute $x$ for it's value of -1, so $x$² would become -1², which would be -1. Or does it not go to that when you change it?

I told you to use parentheses. Then x² for x=-1 becomes (-1)² and there is no ambiguity.

Besides, linking here to another thread you started two separate discussions on the same subject. It always means mess. I am locking this thread.