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/sci/ - Science & Math

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10411359 No.10411359 [Reply] [Original]

Why are rational number superior compare to "real" number system? Have you ever even seen irrational numbers, imho they do not even exist. The completeness axiom is human made bs.
"If a non-empty set A has an upper bound, it has a least upper bound. "

Oh cmon, its like saying that if humans are earthbound then God exists.


Discuss.

>> No.10411361

Do squares exist? Does the diagonal of a square exist?

>> No.10411365

>>10411359
have you ever seen a number like [math] 10^{10^{10}}[/math]? I assume you also believe in Santa Claus?

>> No.10411366

>>10411361
They are geometrical constructs.

>> No.10411371

>>10411365
Given time and a good computer one could print the zeros in screen.

Nobody can never print all decimals of "square root of 2" what ever that even means, 2 isn't a square.

>> No.10411373

>>10411366
And I can say real numbers are numerical constructs.

>> No.10411377

>>10411371
except that there are some ""rational ""numbers"""" that are so large that you couldn't possibly print them out before the heat death of the universe

>> No.10411383

>>10411373
How come? Also, the lenght of 1 m x1 m squares diagonal is not representable as a number.

>> No.10411395

>>10411383
>How come?
Because you can construct real numbers using rationals as a starting point.

>Also, the lenght of 1 m x1 m squares diagonal is not representable as a number.
Only if you insist that real numbers aren't numbers.

>> No.10411400

>>10411395
Rationals are well defined. "Reals" are constructed by literally saying "also irrationals exists besides rationals".

>> No.10411403

>>10411400
>"Reals" are constructed by literally saying "also irrationals exists besides rationals".
Well, that's just factually wrong. Have you ever heard of Cauchy sequences or Dedekind cuts? Have you seen any construction of the reals before? They don't start by saying "irrationals exist".

>> No.10411406

>>10411359
>Have you ever even seen irrational numbers, imho they do not even exist
Math doesn't care if it exists physically or not.

>> No.10411419

>>10411403
Cauchy sequances and Dedekind cuts are just fancy way to say it.

>>10411406
How come?

>> No.10411430

>>10411419
>Cauchy sequances and Dedekind cuts are just fancy way to say it.
So, what you're saying is, constructions of the reals that are well-defined in terms of rationals are bullshit because a consequence of the definitions is that irrationals exist. In other words, you again take as a premise that irrationals don't exist and use that to prove irrationals don't exist.

>> No.10411442

>>10411430
>two algoritms can be as close as wished
>somwhow square root of 2 must exist

>> No.10411451

>>10411419
Math is defined with axioms. Real numbers are structures axiomatically defined to satisfy certain problems. These structures are then assigned to elements in the real world using mappings, which is why they're useful.

>> No.10411452

>>10411419
Pretty much all fields of mathematics rely on some axiomatic system and method of deduction as their foundation. What usually matters is if the system is consistent (does not produce contradictions). A field of mathematics can be consistent without requiring that its objects must be physical. If that is the case, why limit mathematics to what must be physical? The real number may not physically exist in some form or another, but they are still useful because they can help approximate things that are physical.

>> No.10411454

>>10411451
satisfy certain conditions*

>> No.10411466

>>10411400
p-adics

>> No.10411474

>>10411451
>>10411452
But the axioms seems so arbitary. Also for example computers fail to compute 0.1+0.2==0.3. That is why becouse there can be only so many bits in a number. Not infinitely many. What ever that means.

>> No.10411485

>>10411474
>But the axioms seems so arbitary
Axioms are indeed arbitrary. Why should that matter?

>> No.10411496

>>10411474
>But the axioms seems so arbitrary.

Not an argument.

>> No.10411509
File: 195 KB, 1650x1050, 1549413997689.png [View same] [iqdb] [saucenao] [google]
10411509

>>10411359
1/3 doesn't exist, prove me wrong.

>> No.10411671

>>10411359
>>10411359
>Why are rational number superior compare to "real" number system?
Because the rationals can construct the reals
>Oh cmon, its like saying that if humans are earthbound then God exists.
Can you provide a better argument as to why the completeness axiom of the reals is bullshit?

>> No.10411900

>>10411359
Because in the rational standard topology, the function
[eqn] \begin{array}{cccl}f: & \mathbf Q & \longrightarrow & \left\{0,\;1\right\} \\ & x & \longmapsto & \begin{cases} 1 \qquad\text{if } x^2\;\leqslant\;2 \\ 0 \qquad\text{otherwise} \end{cases} \end{array} [/eqn]
is continuous.

>> No.10412519

>>10411509
1/3 = 3/10 + 1/30

>> No.10412549

>>10411371
>1/3 doesn't exist

>> No.10412576

Itt a brainlet can't understand the concept of density and limits.

>> No.10412698

>>10411671
The argument is that it pretty muchs says that irrationals exist too. "If a non-empty set A has an upper bound, it has a least upper bound. "

"set of numbers that satisfy x^2<2 has an upper bound (for example number 2), square root of 2 exist"

Also it assumes that infinite sets exist.

>> No.10412710

>>10412698
>it assumes that infinite sets exist
How many natural numbers are there then?

>> No.10412713

>>10412710
Uncountable

>> No.10412715
File: 150 KB, 480x360, papit.jpg [View same] [iqdb] [saucenao] [google]
10412715

>>10412710
[shows fingers]

>> No.10412765
File: 34 KB, 566x480, read a fucking book.jpg [View same] [iqdb] [saucenao] [google]
10412765

pic related; specifically the first chapter of Pugh's Real Mathematical Analysis.

>> No.10412795

>>10412765
I have read many books from the subject.

I just want to do math without irrationals and infinite sets as these consepts have no basis in reality.

>> No.10412806

>>10411359
>The completeness axiom
>"If a non-empty set A has an upper bound, it has a least upper bound. "
Both these statements can be proved for reals

>> No.10412808

>>10412806
Tell me how you proove an axiom

>> No.10412810

>>10412808
It need not be an axiom sweaty

>> No.10412935

>>10412795
>irrationals
>no basis in reality
Good luck not being able to measure distances.

>> No.10412939
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10412939

>>10412806
>he doesnt know how to define the class of cauchy sequences and mod out the class of sequences that converge to zero, effectively obtaining the real numbers

>He doesnt know that you can find a cauchy sequence that converges to the least upperbound.

>> No.10412968

>>10412939
Why are you quoting me? I know all that.

>> No.10413096

>>10412935
>implying you don't measure by fractions of metre

>implying you don't give answers by fractions of metre

>> No.10413124

>>10411359
>"If a non-empty set A has an upper bound, it has a least upper bound. "
"if a line segment does not stretch to infinity, it has a definite end"
using real numbers you can model geometry on an algebraic object. and time has shown that this is in extremely effective thing to do.

>> No.10413145

>>10413124
If a segment has definite end then we should be able to measure it. But, alas, no measure tape has irrational number printed on them.

>> No.10413261

>>10413145
>If a segment has definite end then we should be able to measure it.
citation needed

>> No.10413532

>>10413145
>if it's not printed on a measure tape, then it doesn't exist
Oh, Lord. The retardation. I guess 0.73639462865394 doesn't exist, then.

>> No.10413640

>>10413532
Well, one could make that kind of measuring tape

>> No.10413933

>>10412519
Prove 1/30 exists

>> No.10414016

>>10413145
do you even know what an irrational number is? why would you print an irrational number on a measuring tape when it infinitely continues without repeating.

>> No.10414113

>>10411474
>But the axioms seems so arbitary.

oh, so you're retarded

jokes on me for expecting anything else

>> No.10414134

>>10413933
A ring with unity by definition contains 1.
Then, it contains 1+...+1=30 by closure of +.

Since Q is a field by definition, and 30≠0 in Q, it has an inverse. This inverse is provably unique, denote it 1/30.

>> No.10414245

>>10414134
Q doesn't exist, otherwise you'd be able to write all the decimals of 1/3 on a piece of paper.

>> No.10414373

>>10411377
those are called dark numbers.

>> No.10414400

> You have to be able to construct a measuring tape with a given number in order for that number to exist.

Lol, you can also use a cylinder to demarcate Pi units. So are we restricting ourselves to straightedge and compass? We can also use the diagonal of a square irl to demarcate sqrt(2) on a measuring tape. If that's your criteria there are a fuckload of irrationals that could be demarcated on a measuring tape. You just watched Norm Memeburgers videos and wanted to seem like you were against the status quo, which is fine, unless it's actually fucking retarded to be against the status quo.

>> No.10414513

Let's just say 1/x has a zero becouse lol so random axioms.

>> No.10414766

this is incredibly stupid

>> No.10415990

If you want stuff that "related to reality" you should go into engineer and therefore to to >>/diy/

>> No.10416018

>>10411474
>Also for example computers fail to compute 0.1+0.2==0.3.
No this is a limitation of whatever (awful) number encoding you are using. There are methods of encoding numbers to arbitrary precision in a computer, but they are less efficient than a good enough approximation with a float/double.

>> No.10416118

>>10413933
1/3 - 3/10 = 1/30

>> No.10417657

>>10411442
What a mess.

>> No.10419208

>>10414245
in ternary if can get you all the "decimals" 0,1 checkmate just because the agreed upon system of representing numbers is not capable of total precision for all possible values does not mean they do not exist. also fractions are just as valid as any other representation

>> No.10419392

>>10411400
No. It is not the same thing to say that
>some irrationals exist
and that
>all irrationals (that the reals consist of) exist
In order to prove the latter you must demonstrate every irrational (i.e. give a unique finite description for each irrational). This is plainly impossible (since the set of finite descriptions is countable but the set of irrationals is uncountable).

At most only a countable subset of the reals can be said to exist. We call these numbers "definable reals". Everything else literally cannot be described.

>> No.10419691

>>10419392
>demonstrate every
same goes for rationals, even just integers

you're a special kind of stupid, aren't you
bless your heart

>> No.10420338

>>10412808
>He's into mathematics and doesn't know modern usage of the word axiom
>He doesn't know what Dedekind cuts are
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