Yes, that is part of the definition of a group.
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∙ 14y agoA set can be closed or not closed, not an individual element, such as zero. Furthermore, closure depends on the operation under consideration.
Yes.
No. It is not a group.
Division, since you can't divide by zero.
In Set Theory: a set is closed under an operation if performance of that operation on members of the set always produces a member of the same set.In Topology: a closed set is a set which contains all its limit points.
A set can be closed or not closed, not an individual element, such as zero. Furthermore, closure depends on the operation under consideration.
No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.
Addition.
addition
yes
Yes, they are.
Please clarify what set you are talking about. There are several sets of numbers. Also, "closed under..." should be followed by an operation; "natural" is not an operation.
Subtraction.
l think multiplication
Yes.
No. It is not a group.
Division, since you can't divide by zero.