0th root

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Guys, I know that the question is not at all on the topic of programming, but … I wrote a program, there was a method written by me that calculates the root of the nth power, and during the test, I had a question: Any number in the zero degree is equal to one, and then what is the zero root of one?


Answer 1, authority 100%

Have you ever encountered 0 0 ? If we consider it as x 0 – then it should be 1, if as 0 x – then zero … I mean that the root of the zero degree can be considered at best only as a limit when the exponent of the root tends to zero – only in this case everything is even worse – the final limit in this case does not exist.

In short, it simply does not exist.

Well, except for x = 1 🙂


Answer 2, authority 67%

I’m not a mathematician, but I would venture to suggest that the very concept of a root of the 0th degree does not make sense. As you know, the nth root of the number x is the number y, which, when raised to the nth power, will give x. That is, y ^ n = x.
At the same time, it is known that the number raised to the zero power is one. Therefore, if x differs from one, then there is no such number that, being raised to the zero power, would give this very x.
Probably, calculus has some answer to this question, but that’s another story


Answer 3

Somewhere above there was a comment that √a = a ^ (1 / n), where n is the degree of the root, I’m only in grade 8, but in my opinion in calculus there is such a thing as uncertainty, this is a theory of limits, it seems , and there you can divide by 0)


Answer 4

When a root is represented as a power, then fractional values ​​are obtained; square root is equivalent to power 1/2, cubic is equivalent to 1/3, etc. As a result, the expression of the degree of the “zero” root 1/0, meaningless from the point of view of mathematics, is obtained. Division by zero as a result of which we get infinity and therefore the root of the zero degree is equal to the inverted eight 🙂

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