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11

1 (6.7%)

10

5 (33.3%)

2

6 (40%)

3

0 (0%)

Potato

3 (20%)

Total Members Voted: 15

[Naturegirl1999]

There are 10 kinds of people in the world: those who understand tertiary, those who don't, and those who were expecting a binary joke.

I like this, what's tertiary?

[Egan_BW]

Like binary, but better. ;D

[Superdorf]

Is base 3: 0-1-2. Thus, "10" indicates 3+0=3; hence the joke.

[Naturegirl1999]

That's cool. Can a computer do tetral code? 0.1.2.3? or is tertiary the most bases right now?

[Egan_BW]

Computers all use bits, except for quantum computers which use something I don't understand. But in mathematics, you can use whatever base system you want.

[Naturegirl1999]

Ah, ok. What is the purpose of other base systems?

[Egan_BW]

To count in.

[Naturegirl1999]

To count in.

Yes, but why not use the default? Why create different base systems?

[Superdorf]

Because we can!

[Egan_BW]

Because base-10 isn't the universal default? It just what our culture settled on. We're not "creating" new base systems, they all already exist and many have been used by humans in the past. I'm sure there's some interesting things you could do switching between them, but I'm not a mathematician.

Besides that, well, binary is obviously useful in computer science, or for counting on your fingers if you don't mind flipping people off. Also useful for understanding other cultures which would use different systems. I don't think mathematicians really need purely practical applications for all they do.

[Naturegirl1999]

I honestly didn't know there were other systems besides base 10 and binary. Would 11 in base 3 become 32? 3 3s and 2? or am I missing something?

[Egan_BW]

0 -   0
 1 -   1
 2 -   2
 3 -  10
 4 -  11
 5 -  12
 6 -  20
 7 -  21
 8 -  22
 9 - 100
10 - 101
11 - 102

Tertiary is counting using the symbols 0, 1, and 2. There is no symbol for 3. Just like in base ten, we have the ten symbols 0 1 2 3 4 5 6 7 8 9. The number ten is represented with two symbols in base ten: 10.

[Devastator]

It's also "Ternary", for the counting system, not "Tertiary."

If you want to translate between bases, here's how it goes:

In base 10, 234 is the same as 2* 10^2 + 3 * 10^1 + 4 * 10^0

The same applies to all other bases, except you change the value of 10.

You can't have a numeral with the same or higher value than the base, because 10*10^2 = 1*10^3, so you'd carry the digit like you were doing arithmetic.

[Naturegirl1999]

Ah, base 10's 12 would be 110 when converted to base 3? This is cool. Is there a math thread for talking about things like this?

[Parisbre56]

I don't see how decimal is supposed to be easier to use, you've got three joints per finger, a second hand to point at one joint on every finger, and even a kid can start memorizing the joints and numbers. +, T, ⊥+, ++, T+, ⊥T, +T, TT, ⊥⊥+ it's so easy. Someone got the idea of using your ten fingers to count to 10 instead, but come on, with ternary you can count from 0 to 242 on one hand, but only to 5 if you stick your fingers up to represent numbers in decimal. What a primitive idea.