Prove that the sum of a rational and irrational number

crossoverman9b

crossoverman9b

Answered question

2022-06-27

Prove that the sum of a rational and irrational number is irrational.

Answer & Explanation

Dwayne James

Dwayne James

Beginner2022-06-28Added 18 answers

We have r R / Q and s Q . Now assume by contradiction that r + s Q . Therefore, there exists such q Q that satisfies r + s = q.

Now let's transfer s. Q is a field, so q , s Q implies r = q s Q , and that's a contradiction to the initial assumption that r Q .

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