If N is a “perfect square” (the square of a “natural number”) and N (x) constitutes all the naturals from 1 to N, than the square root of N shall be the number of perfect squares contained therein that set!

Example:

In the set of all naturals from 1 to 4 or 2^2 than 2 or the square root of 4 is the number of perfect squares contained in that set.

In the set of all naturals from 9 or 3^2 is the the set of all the naturals from 1 to 9 than 3 or the square root of 9 is the number of perfect squares contained therein.

In the set of all naturals from 1 to 100 than 10, or the square root of 100 is the number of “perfect squares” contained in the set of all naturals from 1 to 100.

Proving the axiom that N times infinity shall still equal infinity, and not a greater “infinity”, when N is a natural number [or any positive real]!

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