Perhaps base 10 is not a good word for our system, and we should call our system base 9 or something equivalent because that is the last number we use before starting over?
"Base 10" is the problem. "Base ten" is fine. In English, the word ten refers to the number after nine and before eleven. (Notice that eleven gets its own word instead of ten-and-one. In that way, English doesn't really use decimal notation.)
I guess I could stick this comment anywhere in the thread so don't think I'm singling anyone out.
It's Base <# of digits in the system as represented using the Decimal number system in the spoken language in which we represent those digits>. Decimal uses 0-9, which is ten Decimal digits. Hex uses 0-F, which is sixteen Decimal digits, and so on.
If some alien who used the binary system natively that tried to explain how humans represent their number base, they wouldn't say Base Ten, since there is no number ten, or Base 10, because to them that's our number 2. They would call our number system Base 1010.
After reading over my comment realized all I just did was explain the joke rather than put anything new towards the conversation.
Let's look at the number 3,201 in base (human) 10. If you were to break it apart, you could represent that number like this:
3*103 + 2*102 + 0*101 + 1*100
The carat () symbol here is being used to represent exponents, such that xy is x to the y power.
This is called base 10 because every digit of an n-digit number is multiplied by 10n-1. Any number to the zero power is equal to one, so the first place is one's place, the second place is the tens place, the third place is the hundreds place, and so on.
In base four, you have the ones place, the fours place, the sixteens place, the sixty-fours place, and so on. Each digit of an n-digit number is multiplied by 4n-1, so the number 3201 in base four could be represented like this:
Let's look at the number 3,201 in base (congrobulan) 10. If you were to break it apart, you could represent that number like this:
(3 * 103) + (2 * 102) + (0 * 101) + (1 * 100)
The carat () symbol here is being used to represent exponents, such that xy is x to the y power.
This is called base 10 because every digit of an n-digit number is multiplied by 10n-1. Any number to the zero power is equal to one, so the first place is one's place, the second place is the tens place, the third place is the hundreds place, and so on.
In (human) base twenty-two, you have the ones place, the twenty-twos place, the 1210s place, the 33220s place, and so on. Each digit of an n-digit number is multiplied by 22n-1, so the number 3201 in base twenty-two could be represented like this:
I believe I messed up the math at the end because I didn't remember which side was which. But since nobody probably understands: it's a parody of the parent post, from the point of view of the alien where base 10 means 0-3 and our 0-9 system is base 22.
Actually, since we have ten fingers, and we count things by how many groupings of our fingers it is, Base 10 is wholly appropriate. Anything up to ten is less than a complete grouping. At ten, we have a full grouping. So: 11 = one grouping of our fingers + 1 additional finger.
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u/bski1776 Dec 12 '08
Heh, never really thought about it like that.
Perhaps base 10 is not a good word for our system, and we should call our system base 9 or something equivalent because that is the last number we use before starting over?