Question
Prove that for all $x, y \in \mathbb{R},$ if $x$ is rational and $y$ is irrational, then $x+y$ is irrational.
Step 1
By definition, we can express $x$ as a ratio of two integers, say $x = \frac{a}{b}$ where $a, b \in \mathbb{Z}$ and $b \neq 0$. Show more…
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