Is the set of even integers closed for addition?

- question as answered. Yes, the set of even integers is closed for addition, just as the set of odd integers is closed for multiplication. In my consideration, I take 0 (zero) to be an even integer because 0/2 leaves no remainder. read more

The set of odd number is a subset of the integers; it is not a subgroup because it is not closed; for [math]a\in 2\mathbb{Z}+1[/math] (the odd integers), [math]a+a=2a[/math]; [math]2a[/math] is divisable by [math]2[/math],meaning [math]2a[/math] is even, so the subset is not closed under addition. read more

A set is closed under an operation, if by taking two elements of the set and performing the operation we get a value which is an element of the same set. A set closed under an operation is said to have the closure property for that operation. Closure property of integers under addition: Let a, b are some integers. read more