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Zero to the power of zero

It is determined by definition that 00 ≝ 1, as you cannot calculate it's value.

 


Explanation

In the figure we start with 48 balls on the outer side, and this decreases each time with 8 balls to inner side. Herein we recognize the multiplication table of 8.

0   1   2   3   4   5   6  

According to this calculation the center would have 0 × 8 = 0 balls. That is not true. We have to end on 1, and therefore our formula must read

Number of balls per side = n × 8 + 0n

The correction factor then results in

Side Amount
6 6 × 8 + 0 = 48  
5 5 × 8 + 0 = 40  
4 4 × 8 + 0 = 32  
3 3 × 8 + 0 = 24  
2 2 × 8 + 0 = 16  
1 1 × 8 + 0 = 8  
0 0 × 8 + 1 = 1  

There are good reasons to determine something by definition.

 


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