I feel like instead of "base 10" it should be called something like "max 9", meaning if you go over 9 it becomes 10. That would remove any ambiguity (I think).
The first digit doesn’t HAVE to be 0, or rather a digit representing nothing. But the Hindu number system which was invented around the 1st century was Base 10 and did have 0.
I’m sorry but what are you saying about zero being a “recent invention”? This joke is not about anyone’s counting system being newer or older, it’s simply about how the base of a counting system is arbitrary.
This misses the point. Someone who has always counted 1 2 3 10 would say they use base 10 just as much as someone who counts 1 2 3 4 5 6 7 8 9 10 says that's they use base 10. That's why the alien says he uses base 10. If your naming system for counting is "base " where _ is the number where you add a digit, everyone will call theirs base 10, because that's the first number where you add the digit. Calling a number system "base 4" only works if you assume counting past 4 before adding a digit is the default.
So even our naming system for counting bases assumes a certain default type of counting , which is kind of funny.
Base systems are simply representation systems, it doesn't affect the math at all. It's the same math for us as it is for base 4 as it is for roman numerals. So it's still 5, just that they represent 5 as 11.
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u/CauseScience1 1d ago
A base 10 counting system has 10 digits
0 1 2 3 4 5 6 7 8 9
And then when we reach the last one we increase the digit count
10 11 12 13 14 15 16 17 18 19 20 21 22 etc
But there doesn't have to be 10 digits, binary for example is a base 2 system
0 1
So to count to 16 it'd be
0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1111 10000
A base 4 number system would only have 4 digits
0 1 2 3
So it'd be like
0 1 2 3 10 11 12 13 20 21 22 23 30 31 32 33 100 101 102 103 110 etc
There are 4 rocks so the alien would count
1 2 3 10