there is no closure property of division that applies to integers. ex: 2 divided by 3 is not an integer. what is another example of a set of real numbers that does not have a closure property for one of its basic operations? give an example to illustrate your claim.

Question

myininaya · Answer

what about the positive integers and subtraction
positive integers aren't closer under subtraction
3-4=-1 and -1 is not a positive integer

myininaya · Answer

closed*

anonymous · Answer

yeah but it IS an integer, i need an example that gives me an irrational number

myininaya · Answer

? I thought we were suppose to give a set that wasn't closed under one of its basic operations

myininaya · Answer

why do you want an irrational number?

anonymous · Answer

but addition does have a closure property of basic operations

anonymous · Answer

Square roots?

sqrt(4) = 2

but

sqrt(5) is irrational

anonymous · Answer

but shouldnt it be {+ - x or /}?

anonymous · Answer

No, the sqrt(4) is 2.  I think you are remembering 

Solve:  x^2 = 4

which has solutions 

x = +2 or - 2

anonymous · Answer

ok thanks to everyone that replied, im just gonna go with @myininaya 's reply.. thanks anyway!

phi · Answer

sqrt( negative number) takes you out of the reals.

myininaya · Answer

yes thats true