Can multi digit numbers be made into a single digit using a new base?

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Discussion Overview

The discussion explores the concept of transforming multi-digit numbers into a single digit using a new base. It involves theoretical considerations of number representation, base systems, and the implications of symbol counts in various bases.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant suggests that the base of a digit is defined by the count of symbols available, proposing that any multi-digit number can be represented as a single digit by selecting a new base that is the original base raised to the power of the digit.
  • The participant mentions the necessity of a carry mechanism when adding digits in this new base system, indicating that digits can form a polynomial in the base.
  • Another participant expresses familiarity with the original poster, indicating a personal connection to the topic.

Areas of Agreement / Disagreement

The discussion does not present a consensus, as it primarily consists of a theoretical proposal without extensive debate or counterarguments presented.

Contextual Notes

The discussion lacks detailed mathematical proofs or examples to illustrate the claims made about base transformations and the carry mechanism, leaving some assumptions unaddressed.

Digit
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Digit has {b} ; b is the count of symbols
b is the base of the digit and is the symbol count

b symbols
1 0
2 0,1
3 0,1,2
...
The symbol count is necessary. The symbols can be any set of marks.
If you count and come to the end of the symbols you have, there are 3
choices:
1: give up
2: make another symbol
3: add another digit
If you add another digit you must have a carry mechanism and your digits make a polynomial in b.
It is easy to show that any multi digit number can be made into a single digit by choosing a new base that is old b to the digit power.

I make machines that do math. Anyone interested in this kind of stuff?
 
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Is that you, hlreed?

- Warren
 
Hi Warren.
I thought you would get me.
 
Originally posted by Digit
Hi Warren.
I thought you would get me.
Yes, I probably will.

- Warren
 

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