There are 10 kinds of people

[rwbuild]

After reading all of this I have decided that there only TWO KINDS of people, the living ones and the dead ones.

No, there are three, have you observed some of our illustrious leaders, the walking talking dead heads
And every 1 of them knows 0 so we shall give them 10 out of 10 for knowing zerro

[Carry Pine]

All this talk about binary number systems is confusing. It's all because of this new century. I've been thinking about this century a lot,

MM


Carry Pine

[Pac man]

No, there are three, have you observed some of our illustrious leaders, the walking talking dead heads
And every 1 of them knows 0 so we shall give them 10 out of 10 for knowing zerro

Dont know whether you used "Zerro" on purpose but quite apt for this thread so far!

Urban dictionary definition Urban Dictionary: Zerro:

The ultimate infinitive. One who is in a state of mind which alters perception to achieve a new infinite reality. What is, was, always, and will never be.
"I am Zerro. What you say, do, think, and believe is what I want you to. I exist where I want to exist, and when I want to exist; Forever and ever, always and never."

[swk]

Since we have all the experts in the room can someone tell me how you write 1 in base 1 notation?

oooookay....
I'll have a stab at it.

preliminary warning, this is what I think, I ain't a mathematician and certainly not an expert, but it is a serious attempt. Stop here if you don't like serious! )

All the base-n systems we know use n symbols to represent numbers and are place holder related, eg:

binary (base-2) has two symbols (0&1) and the places represent 2^n ... 2^3 2^2 2^1 2^0 (ie ...8 4 2 1) so for instance binary 1001 = 1x(2^3) + 0x(2^2) + 0x(2^1) + 1x(2^0) = 8+0+0+1 = 9 (in decimal)

ternary (base-3, which was mentioned before) has three symbols (0, 1 & 2) with places representing 3^n ... 3^3 3^2 3^1 3^0 (ie ...27 9 3 1)
so for ternary eg 1021 = 1x(3^3) + 0x(3^2) + 2x(3^1) + 1x(3^0) = 27+0+3+1 = 31 (in decimal)

decimal has 10 symbols (0, 1...9)
hexadecimal has 16 symbols (0, 1...9, A, B, C, D, E & F)

SO, I think base-1 only has one symbol (1) and follows the form: 1^n ... 1^3 1^2 1^1 1^0 (ie ...1 1 1 1)

decimal 1 = 1 (base-1)
decimal 2 = 11 (base-1)
decimal 3 = 111 (base-1)
decimal 4 = 1111 (base-1)
decimal 5 = 11111 (base-1)
decimal 6 = 111111 (base-1)
decimal 7 = 1111111 (base-1) etc... you see how it goes. And no, I can't imagine how zero is represented, but it must exist in base-1 because any base-1 number subtracted from itself must equal zero.

Regards
SWK

[DaveTTC]

im guessing 10 means 2 but I am 1

[Wongo]

SO, I think base-1 only has one symbol (1) and follows the form: 1^n ... 1^3 1^2 1^1 1^0 (ie ...1 1 1 1)

decimal 1 = 1 (base-1)
decimal 2 = 11 (base-1)
decimal 3 = 111 (base-1)
decimal 4 = 1111 (base-1)
decimal 5 = 11111 (base-1)
decimal 6 = 111111 (base-1)
decimal 7 = 1111111 (base-1) etc... you see how it goes. And no, I can't imagine how zero is represented, but it must exist in base-1 because any base-1 number subtracted from itself must equal zero.

Regards
SWK

Sorry this is wrong. For a base-n system to work, you can only have number from 0 to n-1. For example base 10: 0 -9, base 2: 0-1, base 16: 0-F (which is 15). n itself automatically becomes 10.

You failed to follow these rules so there is no point to examine further.

[swk]

Sorry this is wrong. For a base-n system to work, you can only have number from 0 to n-1.

I did a bit more digging as the issue of the zero puzzled me a bit. It seems as though the base-1 system (Unary, I now know it is called!) is a system which has no zero (a bit like the roman numbering system).
So base-1 is the odd one out with the zero rule.

Actually a better way of saying it is there are _two_ types of base-n numbering systems for each n. One with a zero value place holder (surjective? as in Wongo's example) and one without (bijective). Except for base-1 which can only be the bijective system as only one symbol is available (hence no zero can be used).
Isn't wiki a wealth of info...


Regards
SWK

[Wongo]

Wow what an amazing system. 6 sticks represent 6. 7 sticks represents 7.

[Wongo]

In some cultures it is traditional to decorate a birthday cake using the unary system with candles to represent age. This exploits the unique property of the system that there is no requirement for any ordering of the symbols (that is, the age can be read from the candles regardless of how they are arranged on the cake).

Happy birthday Bob. How old are you again, 56? Wait let me get my unary handbook out. Oh 56 equals 56 candles. [sigh...]

[Wongo]

Thinking deeper, I suppose unary is really the most primitive way to represent quantity. As long as you don’t use numbers then I am OK with it.

[A Duke]

So what does this mean to us?

It does not matter how careless you are with your table saw, as long as you have at least one digit left there is a system to let you still count on your finger(s).
Ok so who is coming up with base 0?

Regards

[swk]

Wow what an amazing system. 6 sticks represent 6. 7 sticks represents 7.

Silly as it sounds, it isn't quite as useless as you think. It's actually a big intellectual leap to understand that a stick can represent something else and a bunch of sticks can be used to "record" how many of those other things there may be.

Early shepherds before counting became so common could (for instance) carry a bag of pebbles for the number of sheep they had. Counting off pebbles as the sheep went out in the morning, or in at night made sure there were no strays.

And yes, it becomes very cumbersome very quickly, but for small quantities our earliest ancestors dealt in it was probably good enough. Then the Romans seemed to have used the "tallying" system but introduced short cuts, V for 5, X (two Vs) for 10 , L for 50 etc

Regards
SWK

[A Duke]

And the knights of old used to through a pebble in a heap on the way to battle and pick one up on the way home, what was left in the heap were how many casualties were suffered.
Regards

[tea lady]

decimal 1 = 1 (base-1)
decimal 2 = 11 (base-1)
decimal 3 = 111 (base-1)
decimal 4 = 1111 (base-1)
decimal 5 = 11111 (base-1)
decimal 6 = 111111 (base-1)
decimal 7 = 1111111 (base-1) etc... you see how it goes. And no, I can't imagine how zero is represented, but it must exist in base-1 because any base-1 number subtracted from itself must equal zero.

Regards
SWK

Looks kinda like roman numerals. They didn't have a concept of zero did they?

Thinking deeper, I suppose unary is really the most primitive way to represent quantity. As long as you don’t use numbers then I am OK with it.

Unary? So you on everything so its yours? :

[Pac man]

And the knights of old used to through a pebble in a heap on the way to battle and pick one up on the way home, what was left in the heap were how many casualties were suffered.
Regards

This is also true of jokes in this forum