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### Re: [OT] math fulguration

by salva (Canon)
 on Apr 06, 2021 at 14:27 UTC Need Help??

in reply to [OT] math fulguration

Does some mathematician knows if the above fulguration I had is a known fact?

Yeah, fortunately! That succession of powers is the base of the positional notation used to represent numbers!

So, what do you get when you subtract 1 to a power or 10? a string of nines. What do you get when you do the same to a power of 16 in hexadecimal? a string of F's. What do you get when you subtract one to a power of 2 in binary? a string of ones.

For instance:

```  9000  = 9 * 1000 = (10 - 1) * 10 ** 3
900  = 9 *  100 = (10 - 1) * 10 ** 2
90  = 9 *   10 = (10 - 1) * 10 ** 1
+   9  = 9 *    1 = (10 - 1) * 10 ** 0
-----
9999  = 9 * 1111 = (10 - 1) * 1111

9999
+   1
-----
10000  = 10 ** 4

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