Why do we need other numbers beside 1?

√(-(1+1))

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1

Ok i'll bite. π=?

And how many months?

(1+1)*arctan(1) :^)

Congrats you’ve reached peak autism

For the same reason we don't use binary, why constantly beat yourself with a stick when you simply can stop?

Good thread I enjoyed it

e?

exp(1)

Thats cheating!

Test

Lim_(n1+1+1+1+...) (1+1/n)^n

Feigenbaum constants ?

Unary actually makes some problems intractable, which are otherwise easily solvable in binary or decimal.

Because we're not computers.

Unary is great, some np complete problems have polynomial algorithms when encoding in unary

Best thread I've ever seen on Veeky Forums.

.oO(oh dear god is Veeky Forums really that bad?)

how would you do 1001?

shoo shoo brainlet. Just copy wikipedia defintion replacing any number by a sum of (((1's)))

...

π/1

Your life is worthless user. Just switch to using "0" - number of your life.

1+(1+1+1+1+1+1+1+1+1+1)^(1+1+1)

and before you ask about decimals
1.23 = 1+(1+1)(1+1+1+1+1+1+1+1+1+1)^(-1)+(1+1+1)(1+1+1+1+1+1+1+1+1+1)^(-1-1)

>Why do we need other numbers beside 1?
Convenience.

because 1-(1+1) doesn't equal one so we need another symbol to compress the representations.

Because of (((them)))

...

Nah, exp(x) is easily defined as the unique function f such that f'(x) = x and f(1-1) = 1.

f'(x) = f(x), rather

This desu. The jews keep the goyim confused with all these hard-to-keep-track-of extra numbers.

How do you define a real function if you only have 1?

>We don't but it's more convenient to use different symbols for different numbers.
But what about efficiency?

>this fucking thread
I love this board.

Lack of space, too many 1’s
Sure I have 1 and 1 cupcakes but
1,1,1,1,1 ,1,1,1,1,1,1,1,1,1,1,1,1,1 eggs is too much for me

>”0” - number of your life
What is this equation supposed to equal?

(1+1+1+1)*arctan(1)

How am I supposed to know how many years that is if I can only count to 1?

one one one one one one one one one one one one one one one one one one years

0 is not a number, it's a null value.

We don't. It's a matter of convenience and pragmatism for human-readable representation of info.

>0 is not a number
Uhuh. Numbers represent quantities, and zero is a number that represents a null quantity or nothingness. If you were to say it isn't a natural number, then I agree, but zero is included in plenty of number sets with reason (hint: because it's a number).

It should be (1+1+1+1)*arctan(1) though.

One thing is a number. Another is the symbol or symbols that represent that number.
If you write something like 1+1, you are only using the symbol that represents one, but the number being represented is not one. It's a different number.

what about a half?

or pi?

half: 1/(1+1)
Pi: (1+1+1+1)*arctan(1)

You are using -1 all over this thread too.
Q.E.D KEK.

Why not just define pi as the area of a circle with radius 1?

Better than using 1 to make non-1 numbers

Unary operator applied to 1

Its far less efficient to write one hundred 1s instead of 100, the romans tried it with their numerals and gave up at IV.

((1+1+1+1+1)*(1+1))^(1+1)

>is it possible to write every number using only 1s?
Yes
>should we?

Nice little number game you are playing, but that is still not more efficient than using 100.

ITT we rediscover Succ

okay but what about...

imaginary unit 'i'?
-1/2
the golden ratio (not that important but impressive if you can do it with only ones)

i wont ask for irrational numbers, there an arse to do.

also for the hell of it, just because i wanna see you write it out for redundancy:
Euler's number?

nvm just figered out golden ratio with just ones, its pretty easy, just replace the 5 with (1+1+1+1+1) and the 2 with (1+1)

i = sqrt(-1) duh

e = exp(1)

-1/2 = -1/(1+1)

so after doing some reading ive come to the conclusion that you can perform any maths using just:
>1
>-1
>+
>(parenthesis)
and maybe log and natural log
and probably limits (that you need for things like Golomb–Dickman constant)

also Riemann zeta functions dont work as i can tell yet, i cant get them to work

Chaitin's constant is another problem

this is excluding some irrationals as id assume some finely regressing random ones would/might be impossible.

not sure about 'i' yet, ill get back to you on that

then that just leaves phyical constants which youre boned as things like Planck's constant is pretty much impossible.

quantum shit throws everything out the window as infinite regressing irrational numbers can be done with just ones (unless you pull some crazy shit or get lucky) as there will always be an infinite space where ones cant reach through division that cant be reduced to a finite amount of operations

the Banach–Tarski paradox obviously doesn't work as it makes 1-1+1=2 which wont work logically but does in pure maths.

im actually curiously interested in this
can anyone tell me if im on the right track or not?

wow, im spending way too much time on the internet

oh yeah, wow, im an idiot.

Wouldn't it be more beautiful to use (-1)^(1/(1+1)) instead?

Define the operator

Now get rid of the division with subtraction and change subtraction to adding -1and it's perfect.

Also get rid of the ^power and replace with addition.

(I'm too dumb to do that but I think it's possible.)

Get on my level senpai:
(-1)^((1+1)^(-1))

Are you high?

All I wanna see is 1's, -1's and +'s

As for the being high remark I refuse to answer officer, I'm a sovereign citizen/mathematician, am I being detained?!

-1 is still NOT 1.
If you really want to only use 1 (with substraction as operator), that would be:
(1-1-1)^((1+1)^(1-1-1))

How do you define square root only using + and - faggot?

Fine, just change all -1 in this thread with 1-1-1 just like said.

Fair point.

What about quaternions?

Pseudo polynomial algorithms

Don't math operators count as abstract numbers so that 1-1 is more than 0 under the axioms that must hold?

I mean a (-) != 1, therefore 1-1 is 0 written with 2 symbols, not the 1

What year we are? please write down

Fucking autist, it would be so much easier if you did something like this:
(1+1)^(1+1+1+1) + 1 + 1 + 1 + 1 + 1

easy
(1+1)*((1+1)*(1+1+1+1+1))^(1+1+1)+(1+1)*(1+1+1+1+1)+1+1+1+1+1+1+1

(1+1)*((1+1)*(1+1+1+1+1))^(1+1+1)+(1+1+1)*(1+1+1+1+1)+1+1
ftfy

write infinity with 1 :^)

that's not a number :^)

This but I'd humor you:
absolute(limit(1/x) as x approaches 1-1)

(1+1)*((1+1)*(1+1+1+1+1))^(1+1+1)+(1+1)^(1+1+1+1)+1
come at me bro

no
(1+1)^(1+1+1+1)*((1+1+1/(1+1))*(1+1)*(1+1+1+1+1)^(1+1)+1)+1
longer but more beautiful

>Numbers represent quantities
found the brainlet

1 + 1 + 1 + ... =infinity

men of neolithic were tired about counting their sheep grooving a line for each

Digits were made to avoid exactly this. You are basically writing tally marks which get really annoying when you need to count a lot of something.
You could use scientific notation, but thats a whole other question.

>over 90 replies to a meme thread

that's not bad if you don't consider autistics ones

[math]\sum_{n=0}^{n=\infty}n[/math]
:^^^^^)