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Chadmartigan t1_ix42c72 wrote

So the concept you're digging down is known as the "base" of a number system.

Numbers do not need to be denominated with any particular symbols. We choose those kind of arbitrarily. There have been a lot of number systems that have emerged from different cultures over time, and the ones that stand the test of time do so because they are useful and efficient for communicating information. The Babylonians used a sexagesimal (base 6) system, which did all right for a while, but was ultimately replaced (like virtually all number systems of antiquity) by our current base-10 numerical system, courtesy of the Hindu-Arabic tradition.

So what does it mean for something to be base 6 rather than base 10? In our base 10 system, you know that each digit represents one of ten possible values (0 - 9). In base 6 it's the same, just with fewer values (0 - 5). When you roll over to the next digit in base 10, that next digit represents some power of 10 (10, 100, 1000, etc.) When you roll over to the next digit in base 6, the next digit represents some power of 6 (6, 36, 216, etc.). So, to write the value of "ten" in base 10, we write "10" (1 in the 10's digit plus 0 in the 1's digit = ten). To write the value "ten" in base 6, we write "14" (1 in the 6's digit plus 4 in the 1's digit = ten).

So why did base 10 win out against everything else? Well, in the end, it's useful and easy to work with for a human, for a lot of reasons. It's an even number, so we can halve it easily. We have ten fingers usually, so that makes counting in base 10 sort of intuitive. The value also finds a sort of sweet spot where it can be used to efficiently compute and communicate information. The lower in base you go, the fewer values each digit holds, so a number in a lower base will often take more digits to write than the same number in a higher base. That means higher bases can represent values more efficiently (i.e., with fewer digits) and the computation of numbers (which is traditionally done digit-by-digit, if you're doing it by hand) can be done with fewer steps in a higher base as well. Of course, human calculators don't want too high of a base because then we have to have a deeper library of symbols/values for each digit of our numbers. That makes the scheme more difficult/laborious to learn, and the more symbols you add, the more you rely on nuances in those symbols to distinguish them from one another (which isn't ideal if you're dealing with human calculators).

So to circle back and answer your question, 9 is the "last" value because we use base 10, and we use base 10 because it's a great balance of efficient and intuitive, as time has proven.

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