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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

When squares are built up by successive borders (numbered 1, 2, 3, 4), you get a series of  8, 16, 24, 32, ... etc. bullets.

 
• • •
•   •
• • •
• • • • •
•       •
•       •
•       •
• • • • •
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•           •
•           •
•           •
•           •
•           •
• • • • • • •
• • • • • • • • •
•               •
•               •
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• • • • • • • • •

 

8

16

24

32

So it is easy to find the next numbers. The formula is Sn = 8n. All put together it gives the picture

• • • • • • • • •
• • • • • • • • •
• • • • • • • • •
• • • • • • • • •
• • • •   • • • •
• • • • • • • • •
• • • • • • • • •
• • • • • • • • •
• • • • • • • • •

What must be the formula to fill the hole in the middle? We give the most inner border the number 0. The different powers of zero all give the value 0, except for 00 ≝ 1. If we add this to the formula we get

Sn = 8n + 0n

That produces the series 1, 8, 16, 24, 32, 40, 48, 56, 64 ... etc.

 


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