why does 0 to the power of 0 equal 1?
In: 97
Yes 0^0 is undefined (and sorry, don’t know how to do superscript on mobile so you get carat notation).
However, 0^0 = 1 is convenient in many situations. For example, imagine you’re doing a big, complex calculation on a computer. If you assume 0^0 is undefined, it will go and screw up your calculations.
However, often times, just letting it equal 1 is sufficient. This can be the case for example in some machine learning cases, amongst other things. Letting it be 1 still gives you solid, sensical results, so is it really a problem?
So the real question is, what are you using it for and why does it matter? If you are doing a highly theoretical mathematics proof, it’s probably best to consider it undefined. In some cases, maybe it’s best to consider it as 1. For the machine learning example, if you said it were 0^0 is undefined, or equal to 0, or equal to 50, or anything else, then you risk ruining a perfectly good algorithm.
Furthermore, perhaps there’s some wild scenario where saying 0^0 = 50 could make sense, and any other value is nonsensical. But most often, if you need a concrete value and not just undefined, 1 tends to have the properties that fit the best, even if it’s not mathematically precise.
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