Question: Is infinity a philosophical concept or a real number?

Pamela Docherty answered on 16 Mar 2010:

That’s an excellent question, David. No, it’s not just a philisophical concept: mathematicians work with it all the time and are pretty comfortable with it. It’s not a ‘real number’ either, as it doesn’t obey the rules that we have assigned to real numbers (like 2+1=3, but 2 +infinity=infinity). Because that’s exactly what numbers are: just names someone has assigned to an object, that have to obey mathematical rules. Originally people counted 1,2,3,.. as they corresponded to objects in real life, like sheep, or gold coins. Then 0 was added to our number system (if you want to read about the argument that caused, read the book “Zero – The Biography of a Dangerous Idea” by Charles Seife), then the negative numbers. Infinity is just an extension of this.