Ternary

>>8480837
Fool that you are, ignorant of the superiority of the quaternary system! The truth is quaternary!

>>8480837
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>>8480849
wrong!
every numeral system other than 1,2,3 can be compactly represented by it's smallest base

for quaternary it would be binary
for nonary it would be ternary

As you see in this example I did not go from 3 to 6 but to 9 because 3^2=9, I want to also show with it, that the comprimising of higher numeral systems makes bigger steps (fit more values into a digit) in ternary.

the comparison of how much more values can be packed in ternary digit than binary digit clearly states that ternary is more efficient in this sense.

>>8480849
>not using Nullary

pleb

>>8480889
for 4 you can use 2
for 9 you can use 3
what do you use for 5? How do you compactify that?

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>>8480898
because 5 IS its smallest base, because primes can't be any more compactified, fractional bases can't be computer logic as fractions already require computation.

It can also be that not all bases are turing complete but I'm only guessing maybe someone else knows that.

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bump

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discuss, anyone? :(

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>>8481963
yes, no, maybe so?

>>8482041
oh you.

http://homepage.divms.uiowa.edu/~jones/ternary/hept.shtml

for the ones interested, I think a heptavintimal/septemvigesimal numeral system would be the final form of implimentation for programming.

>>8482084
Sounds interesting. Can you elaborate, anon?

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>>8482086
Well for the simple fact that using three ternary digits (which each have three states) would be the most aesthetic representation to form a trybble.

Don't confuse trybble and nibble and tryte and byte.

because in binary compact representation for the so called nibble represents a smaller information amount than a byte.

In ternary it's the opposite tryte < trybble, regarding the amount of information.

I find most fascinating what brainfuck code would come out of ternary logical operands and what names they'd be given.

A B
0 0
0 1
0 2
1 0
1 1
1 2
2 0
2 1
2 2

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>>8482086
It's not only aesthetics of course, see the increased efficiency implied by radix economy applies to bases but to digits as well, and if three is the most economic base, three digits are the most economic compact representation.

>>8480837
There's a trade off, it's faster on ternary, but you give some factor up. My prof showed me a proof about it freshmen year, don't know remember where it was.

>>8482124
I'll call it the CHAN operation. It is functionally complete.
A B| A CHAN B
0 0 | 1
0 1 | 0
0 2 | 0
1 0 | 0
1 1 | 2
1 2 | 2
2 0 | 1
2 1 | 1
2 2 | 0

>>8482159
>give some factor up

well one factor would be that you wont be able to compute fractions which in decimal have a finite decimal point expression.

so 1/3 would be a finite ternary number while 1/2 would be an infinite ternary

>>8482215
> so 1/3 would be a finite ternary number
So no more 0.999...=1? shitposting?

Where do I sign up?

>>8480907
Turing-completeness is a definition related to symbol-shunting systems. The base is simply how you're encoding the information, and you can represent any piece of information in any base. Bases can't be Turing complete or Turing incomplete, it just doesn't apply.

>>8482215
This is already the case with binary representation, though. You can't represent 1/3 as a finite decimal point expression in base 2. Come to think of it, that's true of decimal as well. There will always be numbers without a finite representation.

It really comes down to which numbers you like the most. Personally I like 1/7, but fuck base 7, I'm sticking with powers of 2

>>8482239

In ternary .2222...=1