# Super Summation 5

## (**x** ≥ **y**)

## This math trick is an obvious sequel to the previous one!

__Examples:__

5^0 + 6^0 + 7^0 + 8^0 + 9^0 + 10^0 + 11^0 + 12^0 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 12 - 5 + 1 = 8

(Notice that there are 8 *1's*!)

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

### Note: If *x* = *y*, then the summation will add up to 1!

### (Actually, if both *x* & *y* are negative, the summation will still have a defined result, but it'll always be positive!)

(-20)^0 + (-19)^0 + ... + (-9)^0 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1= |(-20) - (-9)| + 1 = 12

(Notice that there are 12 *1's*!)

Parentheses were put around the negative numbers to prevent some confusion. **(-20)** - **(-9)** = **-11**, but |**(-20)** - **(-9)**| = **+11**; adding **+1** to **-11** gives you **-10**, but adding **+1** to **+11** gives you **+12**. The vertical line symbols represent *absolute value*, which is always positive. The function of absolute value makes subtraction commutative! Subtraction without absolute value is not commutative.

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© Derek Cumberbatch