Question

prove that the set of positive even integer is countable set​

Answer 1

Answer:

Let f(n)=2n f is 1-1 since if f(a)=f(b) then 2a=2b and a=b. f is onto since if x is even than there is an integer i such that x=2i. Hence the set of even positive integers is countable. Any subset of a countable set is countable.

Answer 2

Answer:

Let f(n)=2n f is 1-1 since if f(a)=f(b) then 2a=2b and a=b. f is onto since if x is even than there is an integer i such that x=2i. Hence the set of even positive integers is countable. Any subset of a countable set is countable.