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One approach to defining infinity is to first define what finite means and then say something is infinite if it is not finite. Rather than define infinity by what it isn't, let's try to define it by what it is.

This definition is intentionally vague, in part because it has precise definitions in math. The sort of thing I want to discuss is what isn't covered in math. A definition of infinity that isn't in terms of what infinity isn't will be motivated by what we think its nature is, will dictate what its nature is, or both.

So let's give it a go...

Infinity is a quality or quantity for which it is possible to be reduced in a way that the reduction is, in some sense, equivalent to the original.

What a reduction is and what it means to be equivalent is, of course, crucial. A particular example of infinity would be an infinite set which is infinite if reduction means removing a single element of the set and two sets are equivalent if there is a one-to-one correspondence between them (i.e., there is a bijection between them).

What it means to be finite could then be a quality of quantity that is not infinite. For example, if reduction means subtraction and equivalence is taken to be equality, no counting number has the quality of infinity since, when reduced, no counting number is equal to the original.

Then perhaps we can answer some basic questions such as is there anything in the universe (or is the universe itself) infinite?