[irishsultan]

It doesn't make sense at all, if you see them as a sequence (which is wrong, sets are not ordered) then after taking the first 3 elements the odd numbers are at 5 and the naturals are only at 3, clearly the odd numbers are approaching infinity faster.

If you don't see sets as a sequence then neither is approaching anything.

[cubefox]

The natural numbers are ordered, yes, that's why it makes sense to talk about how "quickly" they grow. The unordered set theoretical notion of sizes of infinity arguably makes less sense here.