Question

Can anyone prove "The set of positive numbers is open" ?

Answer 1

I'm not sure how much of a proof it would be, but how would you express the set of positive numbers in terms of inequalities?

Answer 2

The set of positive numbers includes all of the numbers down to but not including zero. It includes all the numbers up to and not including infinity.
So, \(0 < x < \infty \), or another way to write it is \((0, \infty)\)
Both ends are open, thus it would be considered an open interval.

That seems pretty trivial though, not much of a proof...

Answer 3

Yeah what i wrote down was more of a definition than the proof.
Thanks for your help though

Answer 4

What class would this be for? I am looking for material, but I want to make sure that the information is relevant / used in that class

Answer 5

it's called "intro to advanced math". Pretty much ALL WE EVER DO are proofs and solving them

Answer 6

unfortunately my prof doesn't believe in text books. He thinks we need to "learn on our own" with no help what so ever. So i have nothing to fall back on. Doesn't help that throughout high school and my beginning years of college, i never learned/worked with proofs until now. I'm always stuck =/

Answer 7

Ah, that sounds difficult. I haven't taken a formal class for proofs, and they often look foreign to me. I have to browse Google to understand them better. ;(

I found this site: http://mathrefresher.blogspot.com/2006/09/open-sets.html
It seems like this may be more useful to a proof...

Answer 8

great! thanks again! =)

Answer 9

You're welcome. Hope that works out! :)