Is the amount of irrationals numbers in between consecutive integers always the same? is this amount infinite?

dannigurl21ck2

dannigurl21ck2

Answered question

2022-11-18

Is the amount of irrationals numbers in between consecutive integers always the same? is this amount infinite?

Answer & Explanation

Ryan Davies

Ryan Davies

Beginner2022-11-19Added 18 answers

If you denote by I n the set of all irrational numbers between n and n + 1, then for any n , m the function f : I n I m given by f ( x ) = x + m n is easily seen to be a bijection. Therefore, the cardinalities of I n and I m are the same.
Widersinnby7

Widersinnby7

Beginner2022-11-20Added 7 answers

Yes. There are many irrational numbers between n and n + 1. I n fact, It equals c = | R | .

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