[nabla9]

What others said, but more abstract and simple way to say it:

Algebra is set of objects and operations on them. Operation is function that gets number of objects as argument and maps it to some other thing

A set has closure under an operation(s) if using those operations on the set members always gives you a member in the same set.

Example:

Natural numbers (0,1,2, ...) are closed under addition and multiplication, because you can't add two numbers and get something that is not natural number. Natural numbers are not closed under subtraction or division because you can get a result that is not a natural number.

[katastic]

>A set has closure under an operation(s) if using those operations on the set members always gives you a member in the same set.

THANK YOU. That line was key and just clicked for me. I'm actually liking everyone's completely-different ways of explaining the same things. When one, or five, are confusing, the sixth may be key to filling in the holes.