[Beyer413]

Hello, I'm in Honors Algebra 2(right after geometry at my school), and I need to define the property of closure. Only problem is, the internet doesn't have it. I just need a really simple defintion. If anyone can help, I'd be forever in debt to you. Thanks.

[Shredcheddar]

From www.wikipedia.org:

In mathematics, the closure C(X) of an object X is defined to be the smallest object that both includes X as a subset and possesses some given property. (Thus, an object is, among other things, a set.) An object is closed if it is equal to its closure.

In algebra, the closure of a set S under a binary operation is the smallest set C(S) that includes S and is closed under the binary operation. To say that a set A is closed under an operation "×" means that for any members a, b of A, a×b is also a member of A. Examples: The set of all positive numbers is not closed under subtraction, since the difference of two positive numbers is in some cases not a positive number. The set of all positive numbers is closed under addition, since the sum of two positive numbers is in every case a positive number. The set of all integers is closed under subtraction.

I've actually never consciously dealt with (or even heard of) this concept, and I'm taking Calculus this semester. From the looks of it, it's just a bunch of math-eze for something relatively simple, but maybe I'm wrong. Either way, good luck.

Here's a more straightforward definition:

"For all a and b in G, a * b belongs to G."