what is the derived, closure and interior set of Irrational numbers?

Question

what is the derived, closure and interior set of Irrational numbers?​

Serenity · Answer

Step-by-step explanation:    ANSWER   ✍️   assume you use the topology derive by the canonical metric in R. then the derive set of the irrational number ¯R−Q is the whole space R. This is just because the irrational number is dense in R,or you can view this as int(Q)=∅. Since Q is dense in R, we have ¯Q=R⇒I∘=R∖¯Q=∅.    All irrational numbers are subset of real number system and it can also be represented on real line. So it is also in real number set. Hence interior of real number set is real number set    hope this helps you!!

Mackenzie · Answer

All irrational numbers are subset of real number system and it can also be represented on real line. So it is also in real number set. Hence interior of real number set is real number

Ariana

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2 thoughts on “what is the derived, closure and interior set of Irrational numbers?”

ANSWER ✍️

assume you use the topology derive by the canonical metric in R. then the derive set of the irrational number ¯R−Q is the whole space R. This is just because the irrational number is dense in R,or you can view this as int(Q)=∅. Since Q is dense in R, we have ¯Q=R⇒I∘=R∖¯Q=∅.

All irrational numbers are subset of real number system and it can also be represented on real line. So it is also in real number set. Hence interior of real number set is real number set

hope this helps you!!

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