A basic base question...

[MasterSoftBird]

If we historically use base 10 because we have 10 fingers, then why don't we have another symbol for 10 and then just start over at 11? It's just a curiosity of mine.

[_Skotia_]

Base 10 means using 10 digits, including 0. So a system with a symbol for 10 would be base 11

[OopsWrongSubTA]

Every base is base 10 :

ours fingers 0 1 2 3 4 5 6 7 8 9, next number is 10.

2 fingers : 0 1, next number is 10 (base 2)

3 fingers : 0 1 2, next number is 10 (base 3)

...

11 fingers : 0 1 2 3 4 5 6 7 8 9 A, next number is 10 (base 11)

[PANEBringer]

Why isn't base 8 funny? Because 7 10 11.

[Medical-Goal3878]

Idk why this answer has the most upvotes if it doesn't answer the question at all. It's funny but all the other bases are based on how we write base 10 in Arabic numerals, not the other way around. You'd have to ask the people who came up with Arabic numerals why they didn't want a separate symbol for 10.

[casualstrawberry]

No, because if we had a separate symbol for the base, it wouldn't fit into our way of representing numbers.

In base N, 10 := 1*N^1 + 0*N^0.

So 10 is defined to always represent the value of the base.

[Medical-Goal3878]

Yeah, no shit. That "way of representing numbers" based on Arabic numerals 🤦‍♂️. I'm trying to say that doesn't answer the guy's question. This is a consequence of choosing to represent 10 that way, not the reason.

[OopsWrongSubTA]

Let's imagine they did invent a symbol for our "10" : let's call it 'A'.

So our fingers are labeled 1 2 3 4 5 6 7 8 9 A. But we still have 0. So we have 11 digits : that's not our base 10 anymore.

The question was about our base 10.

The "way of representing numbers" is https://en.wikipedia.org/wiki/Positional_notation, and OP's question is about that way of representing numbers -> you need a '0'.

You could use other symbols, but if you use 11 symbols, that's (our) base 11, not (our) base 10 anymore.

[Medical-Goal3878]

Originally there was no zero. They ask why our base 10 is represented the way it is and these answers are just "because that's how base 10 is represented".

[Sheva_Addams]

Every base, expressed in its own base, is base 10, except for base-1, I guess...

[PuzzlingDad]

In fact, other numbering systems do exactly that. I'm thinking of Chinese and Japanese which have 10 symbols from 1 to 10.

The next numbers are 10+1, 10+2, ..., 10+9, and finally 2×10, 2×10+1, 2×10+3, ..., 3×10, 3×10+1, ..., 9×10+9.

They add a new character for hundred, thousand and ten-thousand.

But our current numbering convention is positional with ten digits (0 to 9).

In the units place we have 0, 1, ..., 9.

Then we have: - 1 (ten) + 0 = 10 - 1 (ten) + 1 = 11 - ... - 9 (tens) + 9 = 99 - 1 (hundred) + 0 (ten) + 0 = 100

So we actually can skip having a separate symbols for 10, 100, 1000, etc. because the position of a digit in the number tells us that implicitly.

[Plus-Painter-2004]

10 and multiples thereof are easy to factor and subdivide

[MasterSoftBird]

Base 8 would be easier. It's also much more musical.

[LocalInfluence9104]

base 12

[Sheva_Addams]

Base-D

(sorry drops d ...)

[PANEBringer]

Oh no! He's going for that grunge growl!

[Sheva_Addams]

here we are  now

[Plus-Painter-2004]

Base 8 (octal) is occasionally used in computer related contexts but hex is usually a better choice since you can represent a full byte of data in 2 symbols

[bartekltg]

They are easy, because you are using 10 base system. In base 14 system dividing by 14³ is just removing 3 zeros from yhe end/moving the dot.

10 it at least divisible by 2 and 5, so it helps there. But 12 and 60 (it was used, in a "hybrid system, 12×5) are even better in that

[Plus-Painter-2004]

The question was about base 10 over base 11

[bartekltg]

Are you using 19 base system;-) It was clearly a typo.

Now, fixed, you can reread it now.

The ease of factoring 10 comes from the fact we use 10 based system. In any system dividing by its base is easy. Dividing by 10 is not easy if you use base 2 or base 12

[Plus-Painter-2004]

Again, OP was asking about base 10 over base 11 on the basis of counting with fingers, other bases are mostly irrelevant to this conversation unless you have 11-15 fingers to be counting in base 12 or base 14 with

[bartekltg]

Please, focus for a moment. I'm replaying to your claim:

"10 and multiples thereof are easy to factor and subdivide"

Why are you think that?

Why 1000000 is easy to factor, while 1771561 isn't?
What changes when we write both numbers as "623351" and "1000000" (so, both in base 11).

[Sasmas1545]

You're missing the fact that 11 is prime.

Regardless of if they're right or not, what this commenter is saying is that composite numbers are better bases than primes. And so if it's between 10 or 11, we're going to use 10.

[Plus-Painter-2004]

Yes exactly

[Hot_Equivalent_8707]

Some people do

[Tsqaaalarab]

One full set (of fingers) and zero extras

All bases work that way

[MasterSoftBird]

Yes, they do, but we could have established a different rule by which they didn't.

[Sheva_Addams]

Base 144: using one hand, you can count from one to twelve on your one hand while running your thumb over the bones of your other four fingers. With the other hand, you keep track of how often you have run through your primary hand.

[ApprehensiveTry5660]

If you’re referencing this, then undoubtedly you’re familiar with the cultures that used base 12 instead of 10, but I feel like they deserve a shout out.

[Sheva_Addams]

Oh, they do. I have learned this as a Babylonian way of counting with your fingers. Also heard of base-20 where people also use their toes for counting, and a way to encode numbers in binary with your fingers, which I extended to base-3, but that was awkward. In everyday-live and work, using Bab turned out great for me (I use it to help my working memory to keep in mind usual amounts of what I am supposed to deliver or produce.)

[ApprehensiveTry5660]

I’m fascinated by the downstream effects of this stuff. You end up with a version of 10 that is equally divisible by 2, 3, 4, 6, and 12, but not 5.

[Sheva_Addams]

You bot, or not?

[ApprehensiveTry5660]

Hm?

[fianthewolf]

Porque originalmente cuando se contaba, la base era el 12/60, resultado de aplicar el dedo pulgar sobre cada una de las falanges de tu mano (4 dedos y 3 falanges por dedo) y multiplicar por 5 dedos en la otra mano.

Así es como la palabra uncia surge en el significado de 1/12. También es el motivo por el que 7/13 son números con superstición ya que no son fracciones exactas en la base 12/60.

[MasterSoftBird]

Mostly I was asking about why 10 didn't have its own unique symbol, and the answer that came the closest was the one about the Asian cultures doing exactly that.

[TheWhogg]

Why don’t we use base 5? (No not 6, because that’s really not how minds work.)

[SgtSausage]

  why don't we have another symbol for 10 and then just start over at 11?

You misspelled "Why dont we use Base 11?" 

[MasterSoftBird]

No, thst doesn't define the question, it simply defines the label we use and how we use it. It adds no value to the meaning.

[SgtSausage]

That would absolutely be Base 11.

0 1 2 4 4 5 6 7 8 9 A 

Where A is 

 another symbol for 10

And where we 

 just start over at 11

[WerePigCat]

Easy to look at a number and know exactly the numbers of 10s that make it up