Question

Is the set {0,1} closed w/ respect to addition? with respect to multiplication?

Answer 1

As it is relatively easy to find two elements of the set that added together are outside the original set (e.g. 0.8 and 0.9 together is 1.7), the set does not seem to be closed for addition.

Multiplication is a different matter, because you can select any two elements from the original set and the result after multiplication will remain in the set. Therefore this set is closed.

Hope this clarifies a little.