why does 0 to the power of 0 equal 1?
In: 97
Let me try an alternative way of answering this by dropping the mathematical formalism for a second:
Start with the question ‘what is zero?’ A key thing to grasp is that zero isn’t a quantity: it’s the absence of quantity. It’s nothing.
Certain mathematical operations involving zero are meaningful because they correspond to something in reality. The equation 3 + 0 = 3 is meaningful because it represents the real phenomenon that adding nothing to the quantity 3 leaves you with 3.
An exponent is a formal way of designating an iterative multiplication operation. What in reality is designated by “zero to the power of zero”? If translated into an actual operation, it would mean “multiply nothing by itself no number of times.” What would it mean to perform iterative multiplication for no number of iterations? It’s meaningless.
We can formulate all sorts of equations — and even sentences in ordinary language — that are formally / syntactically / grammatically valid but are meaningless as statements (consider the sentence “Purple hope throws humidification at adverbs swimmingly.”). But all that is just talking nonsense. Saying something in mathematics is ‘undefined’ is basically a polite way of saying it is like this.
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