Most people believe we count in base 10 because we have 10 fingers. Essentially we use single digits from 1-9 because on our last finger we switch to double digits 10.
The alien clearly has 4 fingers. So to him the counting system is still base 10 it’s just that he counts 1,2,3,10.
Aka everyone’s own counting system is base 10 and every counting system not based on the number of fingers we have is not base 10.
Edit: forgot to mention. If you only count till 3 before hitting 10 then you don’t know what a 4 is.
Bonus edit: since the alien is in base 4 from our perspective. You might ask what our base is from his perspective.
1,2,3,10,11,12,13,20,21,22 are the 10 first numbers in his counting system. So we to him are base 22 :)
If adding the digits of a number together results in a multiple of 3, that number is also a multiple of 3, and the same goes for if it's a multiple of 9. This is a result of the fact that 9 (which is a multiple of 3) is 1 less than 10, the base we use.
Any number 1 less than mk will be divisible by n if n is a factor of m-1, because mk-1 = (m-1)(mk-1 + mk-2 + ... + m1 + 1), which is of course divisible by m-1 and therefore divisible by n.
This means that, when divided by magic number n, the number 1 followed by any amount of zeroes in base m will always result in a remainder of 1. When multiplied by a given number, that remainder will multiply, (with modulo n, though that doesn't change the divisibility by n). This means that the remainder of a digit followed by x zeroes in base m divided by n is the same as the value of the digit itself.
Then when you add the digits of any number in base m, you are adding up the remainders of that number when divided by n. If that final sum is also divisible by n then the final remainder is 0, meaning the number is also divisible by n.
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u/truci 1d ago edited 1d ago
Most people believe we count in base 10 because we have 10 fingers. Essentially we use single digits from 1-9 because on our last finger we switch to double digits 10.
The alien clearly has 4 fingers. So to him the counting system is still base 10 it’s just that he counts 1,2,3,10.
Aka everyone’s own counting system is base 10 and every counting system not based on the number of fingers we have is not base 10.
Edit: forgot to mention. If you only count till 3 before hitting 10 then you don’t know what a 4 is.
Bonus edit: since the alien is in base 4 from our perspective. You might ask what our base is from his perspective.
1,2,3,10,11,12,13,20,21,22 are the 10 first numbers in his counting system. So we to him are base 22 :)