Sum of 2 irrational numbers, rational or irrational, more?

Audrey Arnold

Audrey Arnold

Answered question

2022-11-20

Sum of 2 irrational numbers, rational or irrational, more?

Answer & Explanation

Teagan Raymond

Teagan Raymond

Beginner2022-11-21Added 14 answers

Given a fixed number z, you can take each q Q and find the unique y q R such that z + y q = q. Since each y q is unique, clearly there are only countably many numbers with that can be found.
So out of the entire pool of | R | things that can go into the y of " z + y", only countably many will yield a rational number, and the rest (uncountably many) will yield an irrational number.

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