Question: given any set of x values, provided they do not repeat...

Question: given any set of x values, provided they do not repeat, can you define a mathematical relationship between them?

yeah just graph in on a computer and fit the curve

computer can't represent irrational numbers accurately, brainlet

What about the numbers 5,17,29. Does a mathematical relationship exist there, no matter how long or complicated it Is? If so, is this true for all sets of numbers?

Yes, you can define relationships between numbers. And they can repeat. It might not be a function, but it is a relationship.

Meant 29 to be 19

what do you mean by between?

Given the set {5, 17, 19} you can define lots of relationships between them. For example: {(5,17), (5,19), (17,19)}.
A relationship between two sets is a sub set of the Cartesian product.

Going from left to right on a graph, is there a way to create one mathematical thought, function or otherwise, to relate every point on a graph, given an infinite number of points, to each other, alsp given no x value repeats.

You can always construct a polynomial equation whose solutions are the numbers.
(x-5)(x-17)(x-19)=0 for example.

>what is curve fitting
>what is interpolation

yes

You can in the sense that the graph does represent a function (i.e. a set of ordered pairs with no repeats in the first entries).

You usually can't come up with some algebraic formula though.

Given enough degrees you can create a polynomial for literally any set of points

any formal system described by mathematicians can, in theory, be programmed, just because the computer isn't physically storing a base representation of a number doesn't mean anything, how do you think Mathematica and other CASes work with pi and e

OK I choose the formal system over the language (0,S,+,*) where the axioms are all true statements of number theory.
Please explain how to program this in a computer.

Of course.
Just map each element to itself, or am I missing something?

Wrong.
It is no problem to do that, you can represent number as a+b*x, for any irrational number x, just like a computer can represent i.

I had the same question some time back, it's all about function approximation, I think.

>Mathematica and other CASes work with pi and e
they approximate them, but can never represent the whole number
>you can represent number as a+b*x, for any irrational number x, just like a computer can represent i
i is not an irrational number retard, computer can represent i because we told him how to do it
irrational numbers require infinite space to be represented accurately

Yes, if we assume the axiom of choice, we can do this for uncountably infinite sets.

>i is not an irrational number retard
I never wanted to imply that. You didn't understand my example.

>irrational numbers require infinite space to be represented accurately
WRONG YOU DELUSIONAL RETARD, LEARN WHAT A CAS IS.
HERE SEE ME REPRESENT AN IRRATIONAL NUMBER IN FINITE SPACE: a=sqrt(2), A COMPUTER CAN DO THAT TOO.
A computer can calculate sqrt(2)*sqrt(2) PERFECTLY USING A CAS, NO APPROXIMATION IS NECESSARY.

>they approximate them, but can never represent the whole number
Wrong you absolute morron, you are uneducated and you should not give your stupid opinion about things which you do not understand.
Google "CAS" and stop being an absolute retard.
Just fucking enter a=sym(2) in matlab and see what happens. SPOILER: NO APPROXIMATIONS ARE MADE AND sqrt(a)*sqrt(a)==2 IS TRUE.

Good lord you are making me angry. Stop talking about things which you do not understand you are embarrassing yourself.

you just described it in a computer.. did you want a regular expression for that language? well first give me one without a program and i'd very happily program it for you.

you're actually retarded, is right and it is you who doesn't understand
now take your CAS and make it display 10↑↑↑↑↑↑↑↑10 first digits of sqrt(2)
oh wait, it can't

>you're actually retarded
At least I know what I am talking about.

> is right
No, he is not.
He has no clue about Computer algebra or CS or math.

>make it display 10↑↑↑↑↑↑↑↑10 first digits of sqrt(2)
Stop shifting the goal post you absolute lunatic.
The claim was that a computer can only calculate approximately with real numbers and is unable to represent them, that is wrong, so wrong that if you seriously believe it you should shut up about computers.
A computer can calculate sin(pi) ACCURATELY to AN INFINITE AMOUNT OF DIGITS.
What they can NOT do is REPRESENT THE DECIMAL REPRESENTATION, which is something VERY different from a (real) number and completely unnecessary to calculate things with them, as any first year student should know.

You don't understand what a CAS is and you don't understand what a computer can and can not do.

>A computer can calculate sin(pi) ACCURATELY to AN INFINITE AMOUNT OF DIGITS

Yes it can.
If you think otherwise you are illiterate.

Go into your matlab and calculate sin(pi), what do you get? As expected you get 1.2246e-16=/=0.
Now take sin(sym(pi)) and like magic you will get 0 and EXACTLY 0 as the result, CAS are truly a miracle.

Yes.