S={x in R∖Q:0<=x<=1} . How would you prove if S is closed or not. I know that there are infinitely many irrational numbers between 0 and 1, and that Q is dense in R, but would that help?

ebendasqc

ebendasqc

Answered question

2022-10-27

S = { x R Q : 0 x 1 } . How would you prove if S is closed or not. I know that there are infinitely many irrational numbers between 0 and 1, and that Q is dense in R, but would that help?

Answer & Explanation

Phoebe Medina

Phoebe Medina

Beginner2022-10-28Added 17 answers

Hint: Q is dense in R if every point of R is either a limit point of Q or belongs to Q. When you form the irrational numbers, you're just removing some of the real numbers (all the rationals). Since between any two real numbers is an irrational number

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