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Take any irrational a where 1/a is also irrational. Then a * 1/a = 1. Even moving from addition and multiplication to exponentials won’t save you: there are ir
by LPisGood 2y ago
Take any irrational a where 1/a is also irrational. Then a * 1/a = 1.
Even moving from addition and multiplication to exponentials won’t save you: there are irrational numbers to irrational powers that are raational.
- pfdietz 2y agoThe nonconstructive proof of that is simple and fun: either sqrt(2)^sqrt(2) or (sqrt(2)^sqrt(2))^sqrt(2) is just such an example.
- School-Cotton 2y ago> Take any irrational a where 1/a is also irrational. In other words: any irrational at all