This is a poorly written proof whose logic is difficult to follow at a glance even for grad students. No one should write a proof this way and I'd discourage popularising it. Here's a clearer version: The RHS has two and only two possibilities. Start by assuming it's rational.
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Let x be irrational. Then we have the second equation above which contradicts the fact that x is irrational, so the assumption must be wrong and RHS can only be irrational.
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As a student I always feared the line “proof is trivial and can be done by the reader as a simple exercise” resulting in hours of hard work. But this comes really quite close to “trivial”....
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demonstration by contradiction
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sınavda düz böyle yazınca 0 alıyoz ama
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Why do we need b and n? Isn't saying r+r always result in r enough?
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I don't understand what *your* question is; the tweet is talking about irrational numbers, but you're only talking about rationals?
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this works with couples too
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When Leslie Clepworth (1956-2016) married Phillip Brentlove (1949-present) few knew that Phillip’s irrational behavior around electric mixers would be passed down to their son Quentin who developed strong aberrant feelings toward his own collection of blenders.
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