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The glyphs $0,1,2,3,4,5,6,7,8,9$ represent the natural numbers from $0$ to $SSSSSSSSS0$. With them, we can write the base-10 representation of any natural number. However, has anyone invented $60$ glyphs for base $60$? We already have $10$ glyphs, so we need $50$ more. I don't want to simply write the digit for, say, $24$ as $a_{24}$, as I consider that cheating, because it uses an underlying base-10 system. Has anyone in any paper or text made up $60$ glyphs? If no one has, I think I will be the first to do so.

Mike
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user107952
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  • Recall that the symbols for hexidecimal are: 0 1 2 3 4 5 6 7 8 9 A B C D E F. Generalize! – David G. Stork Mar 08 '22 at 20:20
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    In the babylonian number system which was base 60, there were digits representing 10,20,30,40,50 and 1 to 9 separately. So a number like 43 would be written as [40][3] where [X] is the symbol for the one of the digits above. You can see what those symbols look like with a quick google search. – Doge Chan Mar 08 '22 at 20:22
  • Probably not, so have fun. :) I suggest to follow arabic tradition for making numerals. Each digit was the number (corresponding to the digit) of angles glued into a shape, so you could see what number the digit represents. I once made digits for 10 and 11 this way to play with base 12. That was fun. :) If you could (re)design all the digits to have additional symmetries, that would be quite awesome and artistic! – P. Grabowski Mar 08 '22 at 20:36
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    When you get to no. 43 it will dawn on you why no-one who has tried so far convinced enough people to preserve their attempts for posterity. But please let us now what you come up with for 42. – Torsten Schoeneberg Mar 09 '22 at 02:25
  • The very first number system beyond simple tally marks almost did. It was invented by the Sumerians, and inherited by the Babylonians much later. It was a positional system much like ours, but with 59 digits. The lack of a $0$ made it somewhat ambiguous. Empty space was sometimes used to denote where we would use $0$ today, but a proper $0$ was invented 2-3 thousand years later in India. Here you can see the digits: https://i.pinimg.com/736x/a1/9d/14/a19d14cde58c213d585f03211f2dde41.jpg. It is derived from a tally system, but the positional usage made it more. – Paul Sinclair Mar 09 '22 at 15:05
  • @PaulSinclair: Looking at that image, I strongly suspect OP would "consider that cheating, because it uses an underlying base-10 system" as well. – Torsten Schoeneberg Mar 10 '22 at 05:35
  • @TorstenSchoeneberg - yes and no. It depends on what you mean by a "base-10 system". Obviously it has tally marks for $1$ and $10$, but when we talk about a "base-10 system", we generally mean a positional system like the one we use. But the 10-tallys are not positional. The Sumerian system is only positional at the base-60 level. In any case, this is clearly not a notation suitable for the OP's purposes, which is why it is only a comment, not an answer. – Paul Sinclair Mar 10 '22 at 13:44
  • Related: https://math.stackexchange.com/q/134990/96384, https://math.stackexchange.com/q/853409/96384 and links there. – Torsten Schoeneberg Nov 08 '22 at 19:03

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