>>9815980You're asking the wrong question..
Math is a set of ASSUMPTIONS and LOGICAL CONCLUSIONS.
There is no rule that dictates wether an logical object exists or not. If you wish to define it, it's there.
The only thing that's intersting is the construction of rules WITHOUT CONTRADICTIONS. I can define:
a = 3
b = 4
a = b
This is perfectly valid in itslef. But if I want to use some more axioms (ie. defining "a" and "b" as natural numbers) to actually get something done, I will soon run into contradictions.
The the more intersting question is:
What happens if we allow or forbid the existence of an empty set?
One problem is that if we don't allow an empty set, we can't reasonably define intersections, because what would be the intersection of {1} and {2} if not the empty set?
All in all we'd lose a lot of powerful properties and operations on sets. So take your empty-set denial back to /pol/ and leave math alone.
