u/Kitchen-Register

I am not good enough at numerical analysis to prove this but intuition (and facts, tbh) would indicate that long division using, for example 7 dividing 1 would be equivalent to 7 dividing 0.99…. This would be a useful way to teach long division (althought students might get confused by 0.9…=1 so the whole thing is moot)

ANYWAY my question is how does one formally prove that division using a dual representation will be exactly the same from a numerical standpoint, without taking it for granted that 0.9…=1. I suppose it would be sufficient to prove 0.9…=1, thought wouldn’t it.

I wrote on an exam:

supA<=supB implies E b in B s.t. a<=b for all a.

my TA says this is wrong. but its not… is it? given any a in A you can pick b>=a to be at least as large as A and his counter example was A=(0,1) and B=(0,1).

I don’t understand.

I had this question posed by a prof today during class…

25 people try out for a highschool volleyball team. 12 must be selected for varsity and 12 for Junior Varsity. How many ways are there to select the teams?

The first part is obvious: 25C12 * 13C12. That’s picking the first 12 then the next 12 into separate groups.

But then I argue you divide by 2 (because you can arbitrarily pick varsity to be the first or second bin) but prof argues that you do not as the order matters… but i don’t understand why given that it’s arbitrary.

Who is right and how do i make sense of this.