I’m too dumb to get it
In: Mathematics
*(This is a bit like those* **”think of a number”** *tricks, where it doesn’t matter what number you start with, the answer always ends up the same. And I’m deliberately putting this into words rather than algebraic notation.)*
* A number to the power 1 is the number itself (by definition).
* Each time you multiply a power of the number by the number itself, you add 1 to the power (again, by definition).
* *This is the first important bit.* Turn that previous statement on its head. To reduce the power by 1, you divide by the number.
* *This is the second important bit.* So. Power 0? The obvious way to get there is to (A) start with power 1, and (B) reduce the power by 1 – because you already know both of those. To reduce the power from 1 to 0, you have to divide by the number.
* But any number to power 1 is just the number itself. And any number divided by itself is simply 1 (except when the number is zero, because dividing by zero is undefined).
* **So any number (except zero) raised to the power 0 is 1.**
((Put a little deeper – this is about the maths having meaning and consistency. Once we’ve defined the concept of positive integer powers *(1, 2, 3, etc.)*, then if the concept of non-positive powers *(0, -1, -2, etc.)* is going to have any meaning *and* give consistent results, those powers have to obey the same rules as the positive ones. And it follows that, to do that, the power 0 always has value 1, for all numbers except zero, as I’ve shown above.))
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