# Super Summation 4

## Because of this fact Brain just mentioned, in the summation formula above, whatever integer you pick to be *x* above the sigma(or summation sign), the sum will always add up to *x*!

__Example:__

1^0 + 2^0 + 3^0 + 4^0 + 5^0 + 6^0 + 7^0 + 8^0 + 9^0 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 1 × 9 = 9

(**1** is the number of multiplicative identity, so *n* × 1 = *n*; notice that there are 9 *1's*!)

The **caret** (^) is the symbol of exponentiation. Raising a *non-zero* number to the power of **zero(0)** always gives you **1**.

You can only pick *counting numbers* to be **x** in this summation formula because **1** is the number below the sigma, to the right of the small **n** & equal sign. All positive integers are counting numbers. (By the way, **zero(0)** isn't a counting number because it's neither positive nor negative; it's *neutral*)

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© Derek Cumberbatch