Paradoxically Speaking

I find paradoxes interesting...
some thoughts...

The Universe is defined as "everything that exists".

It is said that universe is expanding?
Now where is it expanding into? If everything that exists is the universe? There would be nothing left, not even vacuum of space to expand, coz that wud as well be part of the universe.

Counterpoint:
Also if that is so what is present beyond the universe, I mean what after everything.

Need a break...