-A- way of comparing quantities is a 1-1 correspondence.
If you have another and it is logically consistent, then use it. As long as 2 + 2 = 4 it is cool.
y = x if x even, x+1 if x odd. That is a 2-to-1 map/function/correspondence, which implies the set X (all integers) has twice as many numbers as the set Y (even integers).
That is ill defined. What are two sets and what is the mapping.;
Let the two sets be A and B, both subsets of the integers.
Now let x in A. If x is even you say f(x) = x
and if x is odd you say f(x) = x + 1.
if x = x' then f(x) = f(x') now let us check the -inverse-
suppose f(x) = f(x') does this imply x = x'. No
Example f(4) = 4 but f(3) = 4 so the inverse function is not well defined.
So, 4 and 3 which are not equal get mapped into the same element. bzzzzzzzt. Wrong.
So your function as you defined it is NOT a 1-1 onto mapping. It has an ill defined inverse.
Go back and try something else.
or take a course in algebra or set theory.
Do something useful.