SOLUTION: The set of positive real numbers is closed under which operation(s)? is it multiplication HELP!

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
RELATED QUESTIONS
The set of non-zero complex numbers is closed under which operation(s)? (answered by venugopalramana)

The set of integers is NOT closed under which operation? a. Multiplication b. (answered by checkley71)

is the set of real numbers closed under addition (answered by oscargut)

Is the set {-1,0,1} closed under... (answered by KMST)

determine whether each set of numbers is closed under the indicated operation. 1)... (answered by richard1234)

Which set of numbers is not closed under multiplication? odd integers, even integers,... (answered by drk)

Is the following true or false? The set of whole numbers is closed under subtraction... (answered by askmemath)

Which of the following sets of numbers is closed under multiplication? {-2,-1,0,1}... (answered by stanbon)

Is the set of irrational numbers closed under multiplication? I THINK the answer is yes (answered by robertb)