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★ Why is 0 a natural number? Or what is the rationality of designating 0 as a natural number? ★
As a natural number, 0 is neither a prime number (prime number) nor a composite number.

0 is the smallest complete square number.

0 is an even number.

0 is neither positive nor negative, 0 has no opposite number, and the absolute value is itself.

0 times any real number equals 0, and 0 plus any real number equals itself.

0 has no reciprocal and negative reciprocal, a non-zero number divided by 0 has no meaning in the real number range, and 0 divided by 0 has infinite solutions.

The positive power of 0 is equal to 0, and the negative power of 0 and 0 is meaningless.

0 cannot be the true base of logarithm.

The power of 0 is undefined, but it is sometimes taken as 1.