How can I prove that the sum of two irrational

sembuang711q6

sembuang711q6

Answered question

2022-05-15

How can I prove that the sum of two irrational numbers is most likely irrational number?

Answer & Explanation

lutzantsca885

lutzantsca885

Beginner2022-05-16Added 15 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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