Question

Can you help me understand this proof of countable infinity?

Answer 1

answer:Although I have not received this level of math course yet, here is my attempt: First, you must remember part of the definition of a function: no X value can be assigned to two or more Y values, so no two Y values can share an X value. To prove that an infinite set is countable, then there must be a way to assign all of the members of the set to a natural number such that no two members of the set share the same natural number. This means that all countable sets are a results of functions of the natural numbers (even if the functions are transcendental). In the second proof, the first part defines T as any odd number. It then provides a definition of the odd numbers (2K+1), where K can be any natural number. It then points out that this is a function of K, so it concludes that this is a function that can be applied to the natural numbers to generate the odd numbers. This shows that the odd numbers are countable. The first proof is a little harder for me to understand. It may take me a minute or two to figure out, so I’ll post this answer now and then post another when I find the answer.