[orbat]

I can't produce the set of all humans on Earth either, but that doesn't mean they don't exist.

Both real and natural numbers can be reasoned about despite their infinite size (and we even know that e.g. there must be "more" real numbers than natural numbers, even though both sets are infinite)

[jsprogrammer]

The set of all humans is produceable, you simply bound by the planet, or solar system.

There are no bounds in the universe that can contain all the real or natural numbers.