So I have this problem to prove, and I can only satisfy it the first way, I can not bring it back the other way.
- Find a one-to-one correspondence between the set of even integers and the set of all integers. Explain how this shows us that there are the same number of even integers as there are odd integers! Thus, we are showing that ∞ + ∞ = ∞, and thus ∞ does not behave the same as a real number. (Hint: try using the definition of an even number to find a 1-1 correspondence from the integers to the even integers.
I think I can prove it for even numbers to integers, saying that if 2k= an integer where k is an integer, any integer multiplied by another integer = an integer. but how to i prove that there is a 1:1 relationship from integers to even numbers? do i say that 2k= n where k is an integer and n is an even number and k= n/2? that doesnt account for all numbers though right?