So how exactly do you add two irrational numbers?

all NUMBERS have infinitely many cauchy sequence representations. 1 does. 2 does. 1/4 does. and you still know how to add those.

Ok. How exactly is this equivalence relation defined?

en.wikipedia.org/wiki/Construction_of_the_real_numbers#Construction_from_Cauchy_sequences
>Two Cauchy sequences are called equivalent if and only if the difference between them tends to zero.

Pretty retarded if you ask me because the difference of two sequences tend to 0 if and only if the two sequences approach the same value. So basically you are saying:
>two cauchy sequences are equivalent if they converge to the same real number

Which is fine until you realize that you are using cauchy sequences to define real numbers so what the hell are you even doing.

And what are you trying to say, exactly?

>Which is fine until you realize that you are using cauchy sequences to define real numbers so what the hell are you even doing.
what is the problem exactly? the rest of your post makes it seem like you understand it

There are no irrational numbers. If you can't even write it, it doesn't exist. Give me all digits of pi or I dont believe your bullshit.

Real numbers are not defined as Cauchy sequences, they are constructed as Cauchy sequences. Why is this problematic?

You're dumb

Give me all digits of 1/3 or I don't even believe your bullshit about rational numbers existing.

check these irrational numbers

>Give me all digits of pi or I dont believe your bullshit.
en.wikipedia.org/wiki/Approximations_of_π#Digit_extraction_methods

en.m.wikipedia.org/wiki/Chudnovsky_algorithm

not an argument

0.3 repeating

>A: hey bro I fucked Stacy last night!
>B: Sweet! How did it feel have your penis inside her vagina?
>A: Well I got her vagina approximately
>B: What do you mean man? Was it inside or not?
>A: Well the distance between my penis being inside his vagina approached zero
>B: Sooo.. you werent inside her?

I hate when people fucking do this. You didnt even read the definition properly. This is why you fail your exams. The sequences are equivalent if the distance between the corresponding terms of both sequences tends to null. There is no notion of the limit itself.

>not an argument
Correct. It's an observation.

>0.3 repeating
That's only one digit and then a word. Write down every digit now you liar!

Irrational numbers are limits of some rational sequences. Their sum is a limit of sums of elements of these sequences.

"0.3 repeating" contains all the information needed to reproduce the 1/3 exactly

pi doesnt

brainlet btfo

They dont exist but they are useful imaginary concepts, like god.

and en.wikipedia.org/wiki/Approximations_of_π#Digit_extraction_methods gives you an exact formula for each digit of pi

or do you not know how to add rationals?

Take any, answer is the same.

it doesnt because there is no entity in the universe that could use that formula to produce exact value of pi

either the formula is wrong, or pi doesnt exist

let me give you an example
>user's formula
>Whenever you see a girl, punch her into the face
>For every 1000 girls punched into a face, God flips a coin
>If the coin lands on heads, you will be transported to Paradise, where all the girls you punched into their face are reserved eternally for you only
>"Seriously man you can get any girl you want with this formula!"

Pi exist on paper and as a concept in human brains.

left side.

This is equally true of all numbers. There's nothing "different" about the complex numbers, they're all just man-made system of symbols.

in your exemple:
hundreds: 4+1=5
tens: 2+5=7
units: 3+9=12 I keep 2 and add 1 ten
answer 582.

Everything exists on paper and as concept in human brains.

There is a difference, as I think. Humans evolved the ideas of natural numbers, rationals, reals. But it doesnt mean that they accurately represent reality, they represent it as accurate as it was necessary for us to survive and evolve. Reality is something we probably will never figure out, and imaginary numbers are just made up techniques to deal with problems we cant otherwise solve.

Yes, but some are useful and feels logical, and occur in different people's minds, other are not.

Also many paper ideas contradict itself, as, for example, the largest natural number or the largest prime.

There's no entity in the universe that could produce the exact value of 1/3. You lose retard.

> you have three coins
> you lost one
> which part of coins did you lose?

>you are using cauchy sequences to define real numbers
yeah
>the difference of two sequences tend to 0 if and only if the two sequences approach the same value
cauchy sequences on rationals don't need to converge

difference between cauchy sequences = difference between elements.

Notice how this idiot keeps moving the goalposts and contradicting himself:

>You can't write all the digits of pi!
You can't write all the digits of 1/3

>B-but 0.3 repeating contains all the information to do it if you could!
So does the algorithm for p.o.

>B-but you can't write down all the digits...

>how many times can a circle's diameter fit into its circumference

notice how you're still replying to blatant bait and shitting up the board

I don't see all the digits of 1/3 anywhere even though you demanded the same for pi, you must be lying.

It is still questionable that real ideal circles exist. However distinct objects, like coins, exist, so there should exist a way to express how a part of a group of distinct objects relates to the whole group.

0.1 in a system base 3

>pi is not used to describe relationships between real objects
I don't get it. At first you people claim to be mathematical realists but then you try to ignore physics that uses math you don't like.

>reality is something we probably will never figure out
We already have. Just look at cities like New York, services like Facebook, products like Smart Phones. We know how universe works all the way from Big Bang to here.

of course there is largest prime. it is the largest prime humans *currently* knows. when humans find larger prime, then that will be the largest prime. what the fuck?

are you even trying? 1/3 or 0.3 repeating produce it.
there is no question representation 0.3 repeating doesnt solve.
but if i ask you what is the 100923801274891724189789127489th decimal of pi, you are so stupid that you cant even answer that :D

nah, 0.3 repeating is all the digits of 1/3. moving on to next question.

10 in base pi

>1/3 or 0.3 repeating produce it.
So pi or its algorithm produce the exact value of pi. Glad you finally admitted you're wrong.

>nah, 0.3 repeating is all the digits of 1/3. moving on to next question.
No, that's one digit. You said write every digit, not an algorithm.

> New York, Facebook, Smart Phones
It is completely possible that we are just using approximation, which is just accurate enough to create all this stuff, plus many things we have dont require the usage of even real numbers, not even imaginary and so on

If you havent found something, that does not mean that it does not exist. If I have a radioactive source, I cant tell how many atoms decay, but I know that there is a natural number to represent this quantity.

And there are ways to find 100923801274891724189789127489th digits of pi, it is just time consuming.
> i define pi through pi

>I can't tell the difference between a definition and a decimal representation

> I represent pi using pi

>he still confuses representation with definition
Only the latter should not be self referential

1+1-1 = 1

>hurr you can't represent 1 as plus and minus of 1 cuz... uh... dat makes muh face sad

pi=10 in base pi

holy kek

why do you have a picture of steve martin

Very carefully

you can't have a base that isn't a positive integer, makes no sense

in base 10, 134 = 1*10^2+3*10^1+4*10^0
in base 10.5, 134 = 1*10.5^2+3*10.5^1+4*10.5^0

makes sense to me.

itt: massive brainlets who can't accept that math is actually much more well developed than what they previously expected

lmao well played

Put them close to each other and pretend they agree with each other.

a base is a base, you can't say it's only a half

you can't

Of course you can. en.wikipedia.org/wiki/Non-integer_representation

Thanks but I didn't realize someone already said it above me

a base just says how many symbols you can use to represent numbers though. this is something different

I don't think I'm understanding you, I'm talking about a radix.

brush up on your definitions, that is not the definition of a base at all.

I think I get what you're saying, never mind. You can represent numbers using fractions of symbols, as there is no rule against it, and it works out just the same. Also, looking at just the wiki page for radix, en.wikipedia.org/wiki/Radix it mentions at the end how you can use non-natural bases. I do wonder if we could use complex bases, however.