Is math built on assumptions? I just came across this statement when I was lecturing a student on math and strictly speaking I used: 

Assuming that the value of $x$ equals <something>, ...

One of my students just rose and asked me:

Why do we assume so much in math? Is math really built on assumptions?

I couldn't answer him, for, as far as I know, a lot of things are just assumptions. For example:


*

*$1/\infty$ equals zero,

*$\sqrt{-1}$ is $i$, etc.


So would you guys mind telling whether math is built on assumptions?

On a lighter note:
A maths teacher in the UK began a solution to a problem with the words "Suppose $x$ is the number of sheep that solves the problem ..."
only to be asked by a student at the front of the class:
"what if $x$ isn't the number of sheep ...?"
