That is a and b are integers, then a + b is an integer and a * b is an integer? I know it's referred to as closure, but is there a theorem or axiom that says the set of integers is closed under addition and multiplication?

it is just closure. you also have open and closed closures, where the sign comes into play.

Closure is an axiom itself for certain operators, for example since you are referring to integers we can say integers are closed under certain operations (addition, subtraction, multiplication) but not closed under division obviously. Some sets satisfy closures with different operators and so it is useful to be able to identify these things with different number sets. Ie: the positive integers are not closed under subtraction.

If your curious why closure matters you can look up vector spaces.

This post was edited by Xx Shin3d0wn xX on Feb 19 2015 11:17pm

Yeah I took linear algebra last semester. Fuck that class though. And fuck eigen spaces.

Extremely useful class. It's just difficult to recognize it's application or see it's potential in first year.