/sqt/ - Stupid Question Thread

I usually do a couple and stop when I feel like I've grasped the subject and move on to the next chapter. The ones I don't do I mark or write down so I can solve them when I'm revising.

>and an inverse has to be constant
Sure. But it is constant, for fixed a.

You wouldn't say addition isn't invertible because -a isn't "constant".

At a minimum, the identity is always invertible.
>an inverse has to be constant.
But the inverse of x is allowed to depend on x. For example the inverse of 5 in (Z,+) is -5, and more generally the inverse of x is -x.
If you didn't allow the inverse of x to depend on x, then x^{-1} would have the same value for any x' in the group, and by the uniqueness of inverse that means...

Finding an invertible element requires having found the identity for [math]\star[/math]. The identity element, if it exists, must satisfy [math]x = (x-2)(x-2)[/math], ie. [math]x^2 - 5x + 4 = 0[/math], ie. x = 1 or 4. But neither 1 nor 4 are identity elements for [math]\star[/math], since [math]x \star 1 = 2-x[/math], which is not x in general and [math] x \star 4 = 2(x-2)[/math], which is also not x in general. Hence, there is no identity and therefore no invertible elements (because the notion does not make sense without an identity)

"Let G be a finite group. Explain why each row and column of the multiplication table is a permutation of the elements in G."

My thinking so far is as follows:

>a permutation is a reordering of the elements in a set S, or more formally a bijection from S to S
>most rows and columns of multiplication tables contain elements which are not in S, e.g. if S = {1, 2, 3, 4, 5} then row 2 would be {2, 4, 6, 8, 10} and clearly 6, 8, 10 are not in S
>therefore the row is not a permutation, as it does not map back to S
>therefore the question makes no sense, I can't explain something that's wrong
>...

I just checked my notes, I'm a fucking idiot please ignore this post. Except the image, which in retrospect was a great choice.

The multiplication of a group maps into the group (it's the definition of a composition law). The example you chose was not a group law

"le redpill xD" me on biomedical engineering.

Earlier today, there was a discussion about race and intelligence, and I made the point that the races must be similar in intelligence because natural selection does not seem to favor reasoning ability.

Is this correct? I dont really care that much, since I'm not going to change my beliefs about this, but I'm curious what Veeky Forums has to say about it.

I just completed all of Khan Academy math, looking for advice of what to learn next.

Yeh, I should have started with a book but I am but a poor factory hand brainlet and didn't know.