closure property: which set is closed under irrntl addition?

[larry indians27]

can some one help me determine which set of numbers is closed under the indicated operation ?

question: irrational addition

 

[tkhunny]

Re: closure property

What does closure mean? Have you this concept firmly in your mind?

Add an Irational Number to another Irrational number. Is it ALWAYS an irrational number?

There are two ways to go about it. Prove it or find a counter example to DISPROVE it. But first. you must be very clear on your defintiions.

For example:

Natural Numbers
Whole Numbers
Integers
Rational Numbers

Notice how each of these sets of numbers CONTAINS the previous set of numbers. For example, if you add to rational numbers and end up with an integer, does it still have closure? You have to make up your mind before you start. Is this relationship true if the Irrational Numbers? Do they CONTAIN the Rational Numbers? Be sure! No guessing.

Anyway:

\(\displaystyle \sqrt{2} + \left(-\sqrt{2}\right) = 0\)

Does that get us anywhere one way or the other?

 

[larry indians27]

Re: closure property

ya, thanks for the help