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What are some of your unpopular opinions in math? (not about math)
(sh.itjust.works)
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this post was submitted on 18 May 2025
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The exceptions including the number 1. Like it not being a prime number, or being 1 the result of any number to the 0 power. Or 0! equals 1.
I know 1 is a very special number, and I know these things are demonstrable, but something always feels off to me with these rules that include 1.
X^0 and 0! aren't actually special cases though, you can reach them logically from things which are obvious.
For X^0: you can get from X^(n) to X^(n-1) by dividing by X. That works for all n, so we can say for example that 2³ is 2⁴/2, which is 16/2 which is 8. Similarly, 2¹/2 is 2⁰, but it's also obviously 1.
The argument for 0! is basically the same. 3! is 1x2x3, and to go to 2! you divide it by 3. You can go from 1! to 0! by dividing 1 by 1.
In both cases the only thing which is special about 1 is that any number divided by itself is 1, just like any number subtracted from itself is 0
It's been a few years since my math lectures at university and I don't remember these two being explained so simple and straightforward (probably because I wasn't used to the syntax in math at the time) so thanks for that! This'll definitely stick in my brain for now