- #1

Tsunoyukami

- 215

- 11

*Prove that the set of all 2-element subsets of ##N## is denumerable.*(Exercise 10.12 from Chartrand, Polimeni & Zhang's

*Mathematical Proofs: A Transition to Advanced Mathematics; 3rd ed.*; pg. 262).

My idea so far was something like this:

1) Notice ##N## is denumerable since the identity function is a bijective function from ##N## to ##N##.

2) Notice that ##N x N## is denumerable since the Cartesian Product of two denumerable sets is denumerable.

3) The set ##N x N## consists of all ordered pairs of the form ##(a,b)## such that ##a,b \in N## (ie. each ordered pair is "like" a 2-element subset)

4) Every infinite subset of a denumerable set is denumerable.

My difficulty lies in what I have in step (3). I have said "each ordered pair is "like" a 2-element subset" which really isn't precise enough...

I'm not sure if my approach is entirely correct (in fact, I'm pretty sure it's not) but I feel like I'm using all the right facts necessary. Any guidance on how to approach this problem would be appreciated.