Find a subset ofZthat is closed under addition but is not a group of the additive groupZ.

Will the set of natural number be suffice?

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- May 2nd 2010, 01:43 PMMissMouseyClosed Under Addition
Find a subset of

**Z**that is closed under addition but is not a group of the additive group**Z**.

Will the set of natural number be suffice? - May 2nd 2010, 10:00 PMDrexel28
- May 3rd 2010, 03:32 AMMissMousey
Let S be the set of even natural numbers where S = {2, 4, 6, ...}. This will be closed with respect to addition because the sum of two even natural numbers is an even natural number.

However, since the set does not contain inverses and does not contain the identity element, it does not satisfy group properties. - May 3rd 2010, 03:39 AMHallsofIvy
There are two commonly used definitions of the "natural numbers"- all positive integers or all non-negative integers. Either of those will work for this problem.