/sci/ - Science & Math

BTW I'm a girl :3

>>4794320
how is this at all relevant?

>>4794330
>>4794320

He's just a faggot troll tryin' to shit up my thread, pay him no mind.

>>4794320

Yeah, ok, I've answered one of your questions over on /lit/, just and fyi, go over and check it out.

And no, just...no. I mean yes, irrational numbers don't exactly end, however we shorten them to enough decimal places in order for computation to take place effectively without loss of substance to the answer, or allowing error to happen. For example pi is 3.141593. With this sort of definition for an irrational number effective calculations can be made. Also, to redefine an entire number system that we've had for thousands of years to accommodate just a few numbers would be pointless.

But I'm a chemistry major, and I kind of think the whole idea of making a whole new number system to be just plain stupid.

>>4794341

But you don't seem very bright, so your response doesn't do much for me. I'd say thanks for replying, but I wouldn't mean it. :/

People have experimented with a golden ratio base.

http://en.wikipedia.org/wiki/Golden_ratio_base

>>4794354

Well it looks like I wasted my time. Guess I should have scrolled on by when it seemed like an incredibly stupid question to begin with. Have a nice evening.

>>4794372
>thinks something is stupid
>can't explain why
>just wants to be able to call something stupid because that's the only way he can assert himself.

Should have just scrolled by again, friend.

>>4794302
This is not possible. The rationals are countable whereas the irrationals are not, which means expressing the irrationals is strictly more complex than any reasonable scheme of expressing the rationals.

Without boring you with the particulars of a standard second course in calculus at a typical American University, the short answer is there is nothing more convenient than simplying writing the symbol \pi, \eul, etc. That's what the number IS, the decimal expression is a small portion of the convergent series that expresses what the number actually is. So it would be impossible to devise a system more convenient than the one already in use unless there is something more simply than writing a greek letter.

There is a way to deal with irrational numbers. It's called "Real Analysis." I recommend you read an introductory text on Real Analysis for more on pi and e.

But you don't really care about it, so I'm gonna go complete MATH COMP SCI ON THIS BITCH.

You understand natural numbers, integers, and rational numbers I take it. These are represented by sets <span class="math">\mathbb{N}, \mathbb{Z}, \mathbb{Q}[/spoiler], Q for quotient, Z for I don't fucking know.

What about irrational numbers, <span class="math">\mathbb{R} - \mathbb{Q}[/spoiler]? We can divvy those up into two categories: algebraic and non-algebraic. Algebraic irrationals, simply put, are roots to a polynomial. So <span class="math">\sqrt{2}[/spoiler] is the solution to <span class="math"> x^2 = 2[/spoiler]. (Every polynomial has a complex root <span class="math">c\in\mathbb{C}[/spoiler], but we'll not get into that.)

It is difficult to prove that an irrational number is non-algebraic, or "transcendental." But people can prove it. The study of transcendental numbers does exist. How does one go about representing a transcendental in a finite way?

TURING MACHINES.

Turing Machines, basically computer programs, can compute anything computable. They are made of a finite instruction set and infinite memory. You can fit a proof into a Turing Machine because proofs are a method of computation (fo realz yo, it's called Curry-Howard correspondence).

The most important part is that Turing Machines are enumerable. Anything computable is representable as a Turing Machine; i.e. you can represent a number by its infinite process to obtain arbitrary precision.

By the way, you might be interested in Knuth's "surreal number" system. I haven't looked into it much, but it might be what you're looking for

>>4794426
>TURING MACHINES.
>
>Turing Machines, basically computer programs, can compute anything computable. They are made of a finite instruction set and infinite memory. You can fit a proof into a Turing Machine because proofs are a method of computation (fo realz yo, it's called Curry-Howard correspondence).
>
>The most important part is that Turing Machines are enumerable. Anything computable is representable as a Turing Machine; i.e. you can represent a number by its infinite process to obtain arbitrary precision.

God damn cs majors are retarded

>>4794426
That was just.....sad.

>>4794426
>Anything computable is representable as a Turing Machine; i.e. you can represent a number by its infinite process to obtain arbitrary precision.
Which of course means you can only represent computable real numbers this way, which is a countable subset of the real numbers.

>Z for I don't fucking know.
The German word "Zahlen", "numbers".

>>4794426
...now, I might be the one who is off here, it's been a few years since I graduated (comp sci)...but what I'm getting from this isn't making a lot of sense.

So the term Turing Machine, as it is typically used, describes a typical binary computer. Technically it is a certain implementation of a computer, but I don't think that is what you were referring too. Which leave me wondering why you specified them as "Turing Machines" rather than just saying "computer program", as every computer anyone today is likely to be familiar with is a Turing Machine.

So your claim is that a simpler way to represent the various non-simple numbers is by representing them with computer programs. Which seems a bit silly.

I'm not trying to say you're incorrect, I honestly wonder if I'm understanding what you are trying to say correctly. Because I really don't see how this applies to what the OP asked, unless your just saying "use computers not paper for doing math".

>>4794450
Please provide non-computable real number. They exist, certainly. I acknowledge that. But try to construct a non-computable number. I mean construct in the intuitionistic sense.

>>4794453
When you're the only person in a thread that double spaces their sentences and starts new paragraphs haphazardly within a wall of text, we all know you're samefaggin', mon.

>>4794462
Barring that, provide proof that non-computable reals exist?

>>4794457
Impossible, as all intuitionistic-constructable numbers are computable. Which shouldn't be surprising, as both are denumerable.

>>4794460
I don't think that guy is samefagging as Homosexual. I see your point in writing style, but they are different enough to not be significant evidence either way.

>>4794467
When I read them, a long with some smaller posts that don't fit this profile, the voice ton and facial expressions are identical, mon'.

>>4794464
The computable reals are denumerable, because turing machines are. The reals are uncountable. Hence, there must exist incomputable reals.

>>4794426
Conway's surreal numbers. Although Knuth is awesome too.

>>4794464
Turing machines (starting without any input) are countable, real numbers are uncountable. Ergo, since the output of turing machines is enumerable, there must exist a real number which is not the output of a Turing Machine

>>4794460
The only way I could get you to believe he's me is if I say he's the same person as I am. Samefags always lie.

>>4794464
Well, there's
http://en.wikipedia.org/wiki/Specker_sequence

>>4794460
Wait...so I'm same faggin as iamHomosexual...implying he is questioning the veracity of his own post? That doesn't really make much sense.

Did you actually read my question or did you just jump in crying "same fag"?

>>4794474
Then, perhaps all those numbers are the result of Turing Machines WITH inputs?

>>4794481
>2mins apart

Almost!

>>4794486
Stranger than trolling....

Captcha: Logndard called

>>4794483
Those are still denumerable. Unless you allow infinite-length inputs, but that kind of beats the point.

>>4794457
Chaitin's number

>>4794498
So, we don't even know one of the digits in any of the placeholders for any possible configuration? That feels weird man.

>>4794504
Well, non-computable numbers are supposed to be strange.

>>4794506
Could there be a non-computable number where we know it's between 1 and 2 for example?

Alright, whatever. I'm same fagging.

Still hoping for clarification to the questions I brought up in >>4794453

Is there a reason in this circumstance to call programs "turing machines"? (yes I know they are, but it seems an oddly specific and obfuscating use of the word) How does "use computer programs for math" address the OPs question?

>>4794510
Chaitin's constant represents probability, so it's between 0 and 1

>>4794514
We surveyed 100 people. Top 5 answers on the board.
>between 1 and 2

You said:
>between 0 and 1

X

>>4794426
all real numbers are equivalence classes of convergent series of rational numbers. Why does computability even matter if all OP was asking for was alternative ways of representing irrational numbers?

comp sci students are such mean spirited twats always looking for a way to demoralize interested people when the majority of the time they haven't a fuckin clue, at least mathematically speaking. Why not mention floats, that would be an equally as pointless, though relevant to the comp sci mindset, way to obfuscate OP's question.

>>4794626
>obfuscate
>complains about CS fags

>>4794522
chaitan's constant plus k is also not constructible and sits nicely in the interval (k, k+1)