Proof there is an irrational number r in

anniferathonniz8km

anniferathonniz8km

Answered question

2022-05-15

Proof there is an irrational number r in every intervall a < r < b.

Answer & Explanation

Blaine Andrews

Blaine Andrews

Beginner2022-05-16Added 20 answers

For every x , y R there is a bijective function between [ 0 , 1 ] and [ x , y ]
2 2 ] 0 , 1 [
Now when mapping [ 0 , 1 ] onto [ x , y ] 2 2 will also be mapped into the new intervall, therefore there has to be an irrational number in [ x , y ]
2 2 could be mapped onto a rational number. If there are only rational numbers in [ x , y ], then [ x , y ] is countable and is in bijection with [ 0 , 1 ] which is uncountable, which is impossible.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?