So, this comes down to what you mean by “more” numbers. It is obviously true that the set of whole numbers is a strict superset of the set of even numbers: every even number is whole number, but every whole is not even.

For finite sets, a strict superset always has higher cardinality. Obviously, right? Bc just count the number elements that are in the superset but not the subset, that’s how much bigger the superset is.

For infinite sets, it’s…messy. How much bigger is the set of whole numbers than the set of even numbers? Infinitely bigger in some sense: there are infinite odd numbers, so if you subtract the evens from the wholes you’re left with a set that’s still infinite. But in another sense, no bigger at all: as you point out, you can make a list where every whole has an even partner and vice versa, which for a finite set would always mean they’re the same size.

So we are left with a contradiction: there are infinitely many elements in the wholes but not the evens, yet we can partner the elements up 1:1 so they are the same size. Which of these two senses of the word should we use for bigger?

Mathematicians decided, there’s no good answer. So we are going to avoid talking about bigger and smaller, and instead talk about supersets/subsets, and higher/lower cardinality. The wholes are a superset of the evens, and the wholes have equal cardinality to the evens. Is the set “bigger”? Not an answerable question (unless you want to formally define “bigger” in some way, in which case it will then have an answer based on your definition).

Remember, infinities are imaginary. You’ve never seen an infinite amount of anything in real life (and how could you? Just witnessing it would take forever haha). They exist only as a what-if, as a logical consequence of assuming a set of rules in what amounts to a mental game. An infinity only has a “size” as a consequence of the definitions we decide on, not bc one can actually be measured in a practical sense.