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What do you mean by closed?
being closed under these operations means that the result of these operations always returns another integer
I'm not sure - i should know but I'm wondering if 0 is included in the integers I'll have to check If it is then 6/0 is indeterminate so its not closed under division
It doesn't say if 0 is included so I'm assuming it's not
https://www.mathsisfun.com/definitions/integer.html check this out
looks like the answer is no
okay so are integers closed to + - x /
Oh - not just the 0 stops division being closed but for example 10/4 = 2.5 and 2.5 is not an integer so integers are definitely not closed under division
they are closed for +,- and *
now I need to know the same for irrational numbers
they are not closed under multiplication for example sqrt2 * sqrt2 = 2 nor under subtraction for example sqrt3 - sqrt3 = 0