Show that |I|=|R|

Josie Kennedy

Josie Kennedy

Answered question

2022-11-17

Show that | I | = | R |

Answer & Explanation

Abril Orr

Abril Orr

Beginner2022-11-18Added 14 answers

Fix an enumeration of Q , q n , and find a countably infinite subset of I .
Now find a map which fixes all the points which are not r n 's, and maps the union { q n , r n n N } into { r n n N }
bucstar11n0h

bucstar11n0h

Beginner2022-11-19Added 7 answers

R = Q I , so | R | = | Q | + | I | = max ( | Q | , | I | ) = | I | , as the latter is uncountable.

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