Can you please explain this to me? real numbers are "closed" under multiplication?

Question

what exactly does closed mean? thanks for all your help

Answer 1

It means that when you multiply real numbers together, you will always have a real number as your answer.

For example, odd numbers are NOT closed under addition, on account if you add 3 + 5, you get 8 which is even.

Answer 2

Here's all it means:

If you multiply two real numbers together, you'll always get a real number.

If I'm correct, we call it "closed" because the act of multiplying two reals can't get us "outside" of the real numbers.

Sometimes it's easier to understand this property by seeing when it fails:

For instance, the integers are NOT closed under division.  The reason for this is that we can divide one integer by another and end up with one that isn't an integer.

For instance 1/2 = 0.5 (not an integer, so, again, we'd say that the integers are not closed under division).