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Stuff like this makes me feel like the base10 system might eventually get replaced by an even more usefull counting system.
Base 10 strikes me as good tradeoff
Stuff like this makes me feel like the base10 system might eventually get replaced by an even more usefull counting system.
Does it not boil down to a tradeoff between the amount of symbols you are willing to learn and the space you want to use to write a number down ? Base 10 strikes me as good tradeoff
Stuff like this makes me feel like the base10 system might eventually get replaced by an even more usefull counting system.
Base 10: 1,2,5,10
Base 12: 1,2,3,4,6,12
Base 60: 1,2,3,4,5,6,10,12,15,20,30,60
https://en.m.wikipedia.org/wiki/Superior_highly_composite_nu...
Stuff like this makes me feel like the base10 system might eventually get replaced by an even more usefull counting system.
Does it not boil down to a tradeoff between the amount of symbols you are willing to learn and the space you want to use to write a number down ? Base 10 strikes me as good tradeoff
That is, even within the same base, you can have different ways of doing things. "Balanced ternary" is the one that seems like it had the most potential outside of binary, in a computer. That ship has firmly sailed, at this point.
It has the nice property that it's a) binary, and b) each number contains a '11' substring at the end, but nowhere else. This makes it slightly less efficient than the usual base 2 binary, but handles variable length integers nicely; you always know where one number ends and the next begins, so you don't have to worry about overflow or specifying the length of a number.
>"The Quarter-Imaginary numeral system was first proposed by Donald Knuth in 1960. The trick with this base is recognising that powers of 2i "rotate" through the Gaussian plane. " Powers: -1: -(1/2)i, 0: 1, 1: 2i, 2: -4, 3: -8i, 4: 16, 5: 32i, 6: -64 etc. PDS: Now this is highly interesting to me! A system which collapses a 2D number system, that is, non-imaginary + imaginary numbers (AKA, the "Complex (2D) Plane") -…
Nothing surprising here. The cross products of countable set are countable and a bijection between N and NxN which you can then extend as been known for ages. The whole thing falls apart as soon as you use continuous set.
In other words, infinity*infinity=infinity whilst 2^infinity>infinity
The proofs are pretty easy, but that doesn't make the result less surprising to people who don't know it yet.
Stuff like this makes me feel like the base10 system might eventually get replaced by an even more usefull counting system.
Earlier quoted context omitted.
Nothing surprising here. The cross products of countable set are countable and a bijection between N and NxN which you can then extend as been known for ages. The whole thing falls apart as soon as you use continuous set.
The cross product of continuum sets is also equivalent to a continuum, so it does not fall apart, it forms a space-filling curve on complex plane. See z-curve section of https://en.m.wikipedia.org/wiki/Quater-imaginary_base
Stuff like this makes me feel like the base10 system might eventually get replaced by an even more usefull counting system.
Base 12! The operations humans do a lot divide by 2,3,4,12 can be done evenly. Your goal is to pack as many factors into your base as possible. They're called highly composite numbers and their big brother superior highly composite numbers. Base 10: 1,2,5,10 Base 12: 1,2,3,4,6,12 Base 60: 1,2,3,4,5,6,10,12,15,20,30,60 https://en.m.wikipedia.org/wiki/Superior_highly_composite_nu...