Set closed or not closed under addition, subtraction, etc.

[Celsion]

Can anyone explain the concept of that? >_<

[MistaPotta]

For example, let's take the set of odd numbers.

If you multiply an odd times an odd, you get an odd. Multiplying two elements in the set gives you another element in the set. Thus odd numbers are closed under multiplication.

If you add two odd numbers, you get an even. Adding two elements of the set does not give you another element of the set. Thus odd numbers are not closed under addition.

~MP

[AuSmith]

Try proving that the set of numbers with form [unparseable or potentially dangerous latex formula] (a,b are integers) is closed under both multiplication and addition. Actually, this set forms a field, which is what my one graduate class just covered.

[bradp]

Ex. {-1,1} is closed under multiplication/division because
1/1 = 1, 1*1 = 1
-1/1 = -1, -1*1 = -1
-1/-1 = 1, -1*-1 = 1

but it isn't under addition/subtr
-1 + (-1) = -2

[Celsion]

Thanks for all the help! ^_^