Single most important object in mathematics?

[kramer733]

Notations are the most important things in mathematics. With good notation, you can clearly define objects and thus advance through math more.

 

[Char. Limit]

The concept of equality.

 

[wisvuze]

the concept of an "isomorphism"! ( there are tons, but this has got to be in the top bunch )

 

[pwsnafu]

Axioms, definitely. Mathematics is nothing more than applied logic.

Otherwise, I'll fourth (fifth?) the empty set.

*insert offensive generalization about hygiene, women, etc.*.. oh snap!

In physics, the ideal woman is a point particle.

Ok, but then nothing is necessary because you can just change the axioms to make sure they don't exist. So I'm still unsure how the empty set is special in this regard.

So if the empty set doesn't exist, what happens when I take the set of integers and remove all of its elements? What about the singleton set {a} and want to exclude an element?

 

[disregardthat]

Mathematicians, of course.