this post was submitted on 17 Aug 2023
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I still can't wrap my head around why 0^0 = 1
If 0x0=0, and 0^0 is functionally identical to 0x0, why is it 1??
Anything to the power of 0 is 1. For instance:
3^(-2) = 1/9
3^(-1) = 1/3
3^0 = ?
3^1 = 3
3^2 = 9
The pattern here is: Every time the exponent increments, the answer increases by a factor of 3. To get from 3^1 to to 3^2, you multiply 3 by 3 to get 9. Similarly, to get from 3^(-1) to 3^0, you multiply 1/3 by 3 to get 1.
This applies to exponentiation on any base, including zero (briefly checking a few examples, it seems to hold for all real numbers).
0 to the power of anything is 0
0^3 = 0
0^2 = 0
0^1 = 0
0^0 = ?
Technically it's undefined, but in most contexts you're dealing with n^0 rather than 0^n, so it's easier to just say it's 1.
Wikipedia says 0^0 is commonly 1 in algebra and combinatorics, which I have more experience in. It is often undefined in computer science contexts. I was unaware of this, so thank you.
The more I learn, the more I realize there is no one universal math, only different rules which are helpful in different contexts. Thanks for bringing this point up.