Hello

I have some questions about proofs presented while proving that some set is

countable. In Velleman's "How to prove it" , author is trying to prove that there is

a bijection from

to

. He gives the arrangement as shown in the attached figure and then also gives the formula for that arrangement.

and then he asks the reader to show that the above function is indeed a bijection

between the said sets. But I have seen the arguments where people just give the

triangular arrangement as shown in the figure and argue that the arrangement is

one to one and onto between

to

. The wikipedia article on "countable set" has such arguments. My question is , are these valid arguments ? Velleman's way of reasoning seems more rigorous to me. We need to come up with some functional

form of the given arrangement and then prove using usual methods that its a

bijection. Please comment and move this thread to sub forum where its appropriate.

Thanks