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> It also is, for example, the ‘reason’ that 0⁰ equals 1, Is it? That seems different. The math proof for that is pretty easy. a^n * a^m = a^(n+m) Is the ar
by strictnein 8y ago
> It also is, for example, the ‘reason’ that 0⁰ equals 1,
Is it? That seems different. The math proof for that is pretty easy.
a^n * a^m = a^(n+m)
Is the argument just that we should say the above is true if n or m != 0?
- OscarCunningham 8y agoRight, we want to define 0^0 in a way that fits in with the usual rules of exponentiation. The problem is that 0^n is always 0 for nonzero n, but a^0 is always 1 for nonzero a. So 0^0 can't continue both of these patterns by being both 0 and 1. One of the nice reasons to choose 1 over 0 for 0^0 is to make the statement "the cardinality of the set of functions from a size n set to a size m set is m^n". There's exactly one function from the empty set to itself.
- Someone 8y agoAlso, if one claims 0⁰ must equal zero “because multiplying by zero always gives you zero”: there are zero zeroes in the product 0⁰, or, said another way, there are no zeroes in 0⁰. So, why would it have to be equal to zero?