Division by 0, which can also be written as 0.000... (repeating) is not defined.
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division
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
yes
Yes, but only when the denominator is non-zero. Division by 0 is not defined.
The set of rational numbers is closed under all 4 basic operations.