Comment: 2+2

(See in situ)


2+2

2+2=4 is conditionally true.

For K-12 and even college for non-math majors, it is implicitly true; they never tell you about the conditional part that forms the basis of how 2 and 4 are defined. There are a group of axioms that belong to ZF Set Theory : http://en.wikipedia.org/wiki/ZFC

A mathematician who rejects ZFC (yes, they do exist) cannot use 2 or 4 without finding another way to define these numbers. When you write '4', they may ask 'four of what'?

If someone were to discover a contradiction in ZFC, then all the math we were taught in school would be wrong.

The geometry we were taught in school is Euclidean Geometry. There are other flavors that have the potential to wreck all the proofs we did back in grade school.

There are also different levels of infinity, some more infinite than others.