So Z in that funky font is the set of integers, but is there a specific symbol for an integer or do people use Z for that as well?

 

Also is there a symbol or a set of the integers not including 0?

so, [math]\mathbb{Z}[/math] is common to mean the set of integers. You could us any thing you like to denote an integer, but I am sure there will be conventions depending on the area of mathematics used.

 

As long as you state something like

 

[math]x \in \mathbb{Z}[/math]

 

then we all know that [math]x[/math] is an integer.

thanks