Question

prove the set of odd numbers is not bounded above...

Answer 1

Well, what does it mean to be bounded above?

Answer 2

what is the set of odd numbers?

Answer 3

that there is a maximum, but I dont know how to show this in a proof...

Answer 4

odd integers

Answer 5

I think proof by contradiction would be a good start. Assume that there is a maximum -- you can call it M. If indeed the set of odd integers is bounded above, then
\[ M > 2n+1 \] for all n.

Right?

Answer 6

yes, but then can I explicitly say that M < n?

Answer 7

You can say let n = floor(M). This is an integer, so it's perfectly valid.

Answer 8

Then what do you get for your inequality?

Answer 9

M > 2M +1


awesome thank you...

Answer 10

well, strictly speaking its M> 2 floor(M) +1 but in any case, that's impossible, so you have a contradiction. You should also explicitly state that you assume M>0 in the beginning, even though it's obvious.

Answer 11

ok thank you