The cardinality of infinite sets is unintuitive. We can create a one to one correspondence between the Naturals+Sandwich set and the Naturals set (for example, assign sandwich to 0, 0 to 1, 1 to 2, 2 to 3, etc). That means they have the same cardinality.

It's even possible to add an infinite number of elements to an infinite set and retain the same cardinality (the Integers set has the same cardinality as the Naturals set).