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EDIT: markup broke my operators In combinatorics and discrete probability, `0**0 = 1` is a useful convention, to the point that some books define a new version
by red_admiral 2y ago
EDIT: markup broke my operators
In combinatorics and discrete probability, `0**0 = 1` is a useful convention, to the point that some books define a new version of the operator - let's call it `***` - and define `a***b = a**b` except that `0***0 = 1` and then use the new operator instead of exponentiation everywhere. (To be clear, `**` is exponentiation, I could write `a^b` but that is already XOR in my mind.)
So one might as well overload the old one: tinyurl.com/zeropowerzero
This causes no problems unless you're trying to do real (or complex) analysis.
1/0 can cause a few more problems, but if you know you're doing something where it's safe, it's like putting the Rust `unsafe` keyword in front of your proof and so promising you know what you're doing.
- Skeime 2y agoIn analysis, you also use 0**0 = 1 all the time. It's the only sensible convention for power series. It's really just a bit unfortunate that (x, y) -> x**y is not continuous at (0, 0).