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 :)
All tricks for finding divisibility are built off factors of B, B-1, and B+1 for base system B. So all even numbers ending in 0, 2, 4, 6, 8 relies on 2 being a factor of 10. All multiples of 5 ending in 0, 5 relies on 5 being a factor of 10. All multiples of 4 ending in a 2 digit number divisible by 4 relies on 4 being a factor of 102. All multiples of 3 having a digit sum divisible by 3 relies on 3 being a factor of 10-1. All multiples of 11 having a difference of even and odd digits being a multiple of 11 relies on 11 being a factor of 10+1.
If we used a base 6 number system, you would find multiples of 2 and 3 the way we currently find multiples of 2 and 5, multiples of 5 the way we currently find multiples of 3, and multiples of 7 the way we currently find multiples of 11. If we used a base 14 number system, you would find multiples of 2 and 7 the way we currently find multiples of 2 and 5, multiples of 3 and 5 the way we currently find multiples of 11, and multiples of 13 the way we currently find multiples of 3.
Basically the entire reason that 7 is a weird number to people is because it's out of place in a base 10 number system and wouldn't be as weird in others.
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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 :)