Question 53198: The set of positive real numbers is closed under which operation(s)?
is it multiplication
HELP!
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! A set being "closed" under a certain operation means that if you do this operation with any numbers from within the set, can you always get an answer to this operation within the set? It's like "closed shop" in union talk. "Closed shop" in union talk means that you never have to go outside the union to get the job done!
So, if you add two real numbers, do you always get a real number? Yes!
If you subtract two real numbers, do you always get a real number? Yes!
If you multiply two real numbers, do you always get a real number? Yes!
If you divide two real numbers (except zero of course!), do you always get a real number? Yes!!
Therefore, the operations of addition, subtraction, multiplication, and division are all closed for real numbers.
Notice that this is NOT true for addition or subtraction of ODD integers. As you can see, if you ADD two odd integers, you get an EVEN integer, which is NOT within the set of odd integers. However, it is true for MULTIPLICATION of ODD integers, since whenever you multiply ODD integers, you always get an ODD integer.
R^2 at SCC
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