Math, asked by ritu9155, 11 months ago

set of natural numbers N and set of integers Z are closed set.why?

Answers

Answered by Kanitha

the integers are a closed subset of the real numbers. In topological terms, it means that, for any real number that is not an integer, there is an “open set” around it.

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ritu9155: plz dear describe it

Kanitha: A set of natural numbers are(1,2,3....)

Kanitha: Then the complement of the set is (-not defined,0)U(0,1)U(0,2)U....till infinity.

Kanitha: Any union of open set is open

Kanitha: So (-not defined,0)u(1,0)U(0,2)U....is open and (1,2,3........)is closed

ritu9155: thanks dear

Kanitha: Thanks a lot.....

Answered by Anonymous

Originally Answered: The set of natural numbers is a closed set. ... In the topological sense, yes, the integers are a closed subset of the real numbers. In topological terms, it means that, for any real number that is not an integer, there is an “open set” around it.

Hope it's help you! !

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