system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: If infinity is considered as an abstract concept rather than a number, why is zero a number?
gpt
Might sound silly but it's a good question. In fact there was a time when 0 was an 'abstract concept' in the sense that it didn't really exist in it's own right as a number (a couple of millenia ago). 

To answer this question, it's best to understand that maths is axiomatic, in other words it's based on a few fundamental rules on which all the other rules are built upon. For example one of the rules for addition is that a + b = b + a. This might seem trivial but this along with a few other basic rules entirely define the rules of arithmetic and allow us to build theorems and understand numbers at a deeper level. 

The very first of Peano's axioms (which are still mostly used today) is that 0 is the first natural number. This might not be a satisfying answer, but it's this definition which has allowed the many fields of mathematics to be consistent.

The definition of infinity on the other hand, while still rigorous is a lot less clear because it can take nuanced differences depending on which field of maths you are talking about. Furthermore not all infinities are the same size! As we can't put any number value on it, it remains a more 'abstract concept'.