What Does 'Closed Under Addition' Mean in Mathematics?

[garyljc]

What does it means by closed under addition
For eg : As S is closed under addition
S = {gn : n is a member of integers}
could anyone elaborate more on this and gimme some example ?

Does it mean that when something is closed under addition , we only consider addition and nothing else ?

 

[arildno]

What does it means by closed under addition
For eg : As S is closed under addition
S = {gn : n is a member of integers}
could anyone elaborate more on this and gimme some example ?

Does it mean that when something is closed under addition , we only consider addition and nothing else ?

"Closed under addition" means that the sum of two integers is an integer.


Note, for example, that the integers are NOT closed under the operation of division, or for that matter, closed under square root extraction.