/sci/ - Science & Math » Thread #13324504

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Anonymous Fri 25 Jun 20:09:06 2021 No.13324504 View Reply Original Report

Quoted By: >>13324512 >>13324514 >>13324674 >>13324692 >>13326214 >>13326576 >>13330325 >>13331710 >>13331762 >>13332557

On the subject of .9999... = 1, does that imply that every number has a rational and irrational form? Can all natural numbers be represented in more than one way?

Anonymous

Anonymous Fri 25 Jun 2021 20:11:21 No.13324512 Report

Quoted By: >>13324520 >>13325757

>>13324504
>.9999...
is rational form

Anonymous

Anonymous Fri 25 Jun 2021 20:12:22 No.13324514 Report

Quoted By: >>13324520 >>13327222

>>13324504
>Can all natural numbers be represented in more than one way?
1
1/1
2/2
3/3
4/4
5/5
6/6
7/7
0/0

Anonymous

Anonymous Fri 25 Jun 2021 20:14:22 No.13324520 Report

Quoted By: >>13324540 >>13325757

>>13324512
1 is the rational form
>>13324514
Can the same value be represented in both a rational and irrational way.

Anonymous

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Anonymous Fri 25 Jun 2021 20:18:40 No.13324540 Report

Quoted By: >>13324554 >>13324586

>>13324520
>Can the same value be represented in both a rational and irrational way.
Yes. There are special numbers that belong to the intersection of rational and irrational numbers.

Anonymous

Anonymous Fri 25 Jun 2021 20:22:09 No.13324554 Report

Quoted By: >>13324568

>>13324540
I take it pi is an example of this? And are these numbers supposed to be transcendentals or a different type of number?

Anonymous

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Anonymous Fri 25 Jun 2021 20:25:18 No.13324568 Report

Quoted By: >>13324574 >>13324575 >>13324586 >>13328737

>>13324554
Yeah, exactly like pi! It's irrational if you write it out, but it is also the ratio of the perimeter and the diameter of a circle. Similarly the golden ratio is RATIOnal but also irrational.

Anonymous

Anonymous Fri 25 Jun 2021 20:26:40 No.13324574 Report

Quoted By: >>13324580

>>13324568
The golden ratio is the most irrational number. You're spouting nonsense.

Anonymous

Anonymous Fri 25 Jun 2021 20:27:06 No.13324575 Report

Quoted By: >>13324580 >>13324651

>>13324568
Would imaginary numbers be considered rational or irrational?

Anonymous

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Anonymous Fri 25 Jun 2021 20:28:16 No.13324580 Report

Quoted By: >>13324586 >>13324592 >>13324601

>>13324574
If that wasn't already obvious from me saying there are numbers in the intersection of rationals and irrationals, then either you skipped that part or you may be a bit slow today.

>>13324575
I'd call them emotional.

saged

saged Fri 25 Jun 2021 20:29:10 No.13324586 Report

Quoted By: >>13324595

>>13324580
>>13324568
>>13324540
keep watching anime, anime poster

Anonymous

Anonymous Fri 25 Jun 2021 20:30:39 No.13324592 Report

Quoted By: >>13324615

>>13324580
Also regarding irrationals, do they usually represent the sums of infinite sequences? Ex: pi = 4-1/3+1/5-1/7+1/9... or e with that sequence.

Anonymous

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Anonymous Fri 25 Jun 2021 20:31:18 No.13324595 Report

Quoted By:

>>13324586
I haven't watched any since maybe November or early December.

Anonymous

Anonymous Fri 25 Jun 2021 20:34:11 No.13324601 Report

Quoted By: >>13324615

>>13324580
You claimed pi and phi are in the intersection of rationals and irrationals. Even if we ignore the fact that this intersection is empty, phi is the opposite of rational.

Anonymous

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Anonymous Fri 25 Jun 2021 20:38:50 No.13324615 Report

Quoted By:

>>13324592
Take some sequence converging to your favourite irrational number. Then define a new sequence by letting the first entry be the first entry of your original sequence. For the later entries, you'd then do some sum tricks which I'm too tired to formulate now. Then the series with those entries as its inputs should have the same limit as your original sequence.

>>13324601
Thanks for the remarkably new piece of information!

Anonymous

Anonymous Fri 25 Jun 2021 20:53:09 No.13324651 Report

Quoted By: >>13324684

>thing is defined by a ratio
>therefore it must be rational
That's not what "rational" means.

>>13324575
Algebraic. Specifically, the imaginary unit is the solution to the polynomial x^2 + 1, just like the square root of 2 is the solution to the polynomial x^2 - 2.

Anonymous

Anonymous Fri 25 Jun 2021 21:03:34 No.13324674 Report

Quoted By:

>>13324504
>.9999... = 1
Both sides are rational because it’s 1

Anonymous

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Anonymous Fri 25 Jun 2021 21:08:24 No.13324684 Report

Quoted By: >>13326295

>>13324651
>Specifically, the imaginary unit is the solution to the polynomial x^2 + 1
It's _a_ solution. That polynomial has two roots.

Anonymous

Anonymous Fri 25 Jun 2021 21:13:22 No.13324692 Report

Quoted By:

>>13324504
All numbers have an infinite decimal expansion, a certain subset of those also have a finite decimal representation.

Anonymous

Anonymous Fri 25 Jun 2021 21:14:16 No.13324695 Report

Quoted By:

this thread is full of retardation.

Anonymous

Anonymous Sat 26 Jun 2021 02:19:57 No.13325757 Report

Quoted By: >>13325832

>>13324512
>>13324520
if .9999... and 1 are the rational forms, what's the irrational form?

Anonymous

Anonymous Sat 26 Jun 2021 02:46:49 No.13325832 Report

Quoted By:

>>13325757
no such thing

Anonymous

Anonymous Sat 26 Jun 2021 02:55:51 No.13325859 Report

Quoted By:

anime girls are pretty, what IQ do I need to date one

Anonymous

Anonymous Sat 26 Jun 2021 05:06:05 No.13326157 Report

Quoted By: >>13334803

It's funny how decimal notation breaks the brains of so many here.

Anonymous

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Anonymous Sat 26 Jun 2021 05:31:39 No.13326214 Report

Quoted By:

>>13324504
There might be something to this. Im going to work it out.

Very interesting hypotheses anon

Anonymous

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Anonymous Sat 26 Jun 2021 05:55:39 No.13326274 Report

Quoted By:

the biggest takeaway here is that a number can be
1) well-defined
2) non-uniquely represented
so this permits the possibility of a well-defined quotient 0/0 which is not uniquely represented in R.

Anonymous

Anonymous Sat 26 Jun 2021 06:04:32 No.13326295 Report

Quoted By: >>13326567 >>13326769

>>13324684
regarding pic rel: if n! is an integer, and if you can take an arbitrarily large n and still have n! be an integer, then shouldn't pi also be an integer?

Anonymous

Anonymous Sat 26 Jun 2021 07:27:41 No.13326526 Report

Quoted By: >>13330298

The representation is unique EXCEPT at near wholes where N.99999...=N+1.

Anonymous

Anonymous Sat 26 Jun 2021 07:44:58 No.13326567 Report

Quoted By: >>13326882

>>13326295
n! is always an integer, n!/(2n+1)!! is not.

Anonymous

Anonymous Sat 26 Jun 2021 07:49:10 No.13326576 Report

Quoted By: >>13328653

>>13324504
there is no such thing as "irrational form" or "irrational notation"

Anonymous

Anonymous Sat 26 Jun 2021 09:27:16 No.13326769 Report

Quoted By:

>>13326295
You should probably go redo your third grade math.

Anonymous

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Anonymous Sat 26 Jun 2021 10:26:07 No.13326882 Report

Quoted By: >>13327019

>>13326567
so you admit is rational since it's the quotient of two integers.

Anonymous

Anonymous Sat 26 Jun 2021 11:49:09 No.13327019 Report

Quoted By:

>>13326882
I just clarified that the terms were not integers.
Summation is going to infinity, there is a limit there so its not as simple as that.

Anonymous

Anonymous Sat 26 Jun 2021 13:53:29 No.13327222 Report

Quoted By:

>>13324514
0/0 != 1

Anonymous

Anonymous Sat 26 Jun 2021 21:45:48 No.13328653 Report

Quoted By: >>13328690

>>13326576
Would the term be transcendental or complex?

Anonymous

Anonymous Sat 26 Jun 2021 21:56:34 No.13328690 Report

Quoted By:

>>13328653
Neither. Transcendental numbers are those which cannot be expressed as the root of a polynomial with integer coefficients.
Complex numbers are either square roots of negative numbers or non-principal nth roots of real numbers.

Anonymous

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Anonymous Sat 26 Jun 2021 22:08:07 No.13328737 Report

Quoted By: >>13328759 >>13328760

>>13324568
Why are pi and phi called "irRATIOnal" numbers if they are both ratios
We're being played for absolute fools by the mathematical establishment

Anonymous

Anonymous Sat 26 Jun 2021 22:15:41 No.13328759 Report

Quoted By:

>>13328737
Blame the people who read the Greeks and thought it would be a good idea for it to only refer to "ratio of integers"
Actually never mind, that was a good idea; keeping the word "ratio" in terms like "golden ratio" was not

Anonymous

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Anonymous Sat 26 Jun 2021 22:16:27 No.13328760 Report

Quoted By:

>>13328737
Just between you and me, I'm starting to believe that there's no rationale for that...

Anonymous

Anonymous Sun 27 Jun 2021 12:48:18 No.13330298 Report

Quoted By: >>13330330

>>13326526
Wrong. For example

0.5 = 0.4999...

Anonymous

Anonymous Sun 27 Jun 2021 12:55:38 No.13330325 Report

Quoted By:

>>13324504
The fact that 0,99...=1 was the main dedekinds counterargument to explain thay the function that cantor gave to biyectively map a line into a square was not a biyection

Anonymous

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Anonymous Sun 27 Jun 2021 12:57:00 No.13330330 Report

Quoted By: >>13330340 >>13330377

>>13330298
But, anon, if 1 = 0.999..., then 0.5 = 0.454545...

Anonymous

Anonymous Sun 27 Jun 2021 13:00:29 No.13330340 Report

Quoted By: >>13330344

>>13330330
Dude whenever two real numbers are not equal there is always somebody between them. Tell me who is between 0,999.. and 1

Anonymous

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Anonymous Sun 27 Jun 2021 13:01:35 No.13330344 Report

Quoted By:

>>13330340
You know (((who))).

Anonymous

Anonymous Sun 27 Jun 2021 13:15:14 No.13330377 Report

Quoted By: >>13330381

>>13330330
.9/2 = .45
.09/2 = .045
.009/2 = .0045
Add them up you get .4995 and then continue likewise.
Your answer comes from misplacing decimals when you divide by 2.

Anonymous

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Anonymous Sun 27 Jun 2021 13:17:01 No.13330381 Report

Quoted By: >>13330431

>>13330377
I know!

Anonymous

Anonymous Sun 27 Jun 2021 13:34:49 No.13330431 Report

Quoted By:

>>13330381
YWNBAW

Anonymous

Anonymous Sun 27 Jun 2021 20:23:27 No.13331710 Report

Quoted By: >>13331725

>>13324504
They are two different points on axis, with 0 distance in between. Finally, understand real numbers, please.

Anonymous

Anonymous Sun 27 Jun 2021 20:27:21 No.13331725 Report

Quoted By:

>>13331710
>They are two different points on axis
they are the exact same point

Anonymous

Anonymous Sun 27 Jun 2021 20:36:09 No.13331762 Report

Quoted By: >>13331911

>>13324504
>does that imply that every number has a rational and irrational form
obviously not. 0.999... is clearly rational and exactly equal to 1.

Anonymous

Anonymous Sun 27 Jun 2021 21:15:30 No.13331911 Report

Quoted By: >>13332316

>>13331762
can you represent the same value in a rational and irrational way?

Anonymous

Anonymous Sun 27 Jun 2021 22:43:17 No.13332316 Report

Quoted By: >>13332541

>>13331911
no

Anonymous

Anonymous Sun 27 Jun 2021 23:33:52 No.13332541 Report

Quoted By: >>13332963

>>13332316
What if I just subtract the irrational value from a whole number, and use that relation to denote a rational value? Like 4-pi + pi-3 = 1?

Anonymous

Anonymous Sun 27 Jun 2021 23:39:34 No.13332557 Report

Quoted By: >>13332875 >>13332883 >>13334092 >>13334871

>>13324504
>.9999... = 1
On this subject, does this imply that any object (metaphysical) which infinitely approaches another object is identical to the object which it approaches?
Or is this merely number trickery that has no meaning outside of the mental masturbation of pure mathematics?

Anonymous

Anonymous Mon 28 Jun 2021 01:30:18 No.13332875 Report

Quoted By: >>13332966

>>13332557
>any object (metaphysical) which infinitely approaches another object is identical to the object which it approaches?

No
0.999999 is ALWAYS approaching 1.01
BUT it is always a finite distance away (always at least .01 away).

Anonymous

Anonymous Mon 28 Jun 2021 01:33:30 No.13332883 Report

Quoted By: >>13332902

>>13332557

You want to say. If two numbers have no finite distance between them then they are the same number.

Anonymous

Anonymous Mon 28 Jun 2021 01:43:44 No.13332902 Report

Quoted By: >>13334488

>>13332883
Does that mean infinity is the same as 0? Or that they work using a similar mechanism or concept?

Anonymous

Anonymous Mon 28 Jun 2021 02:05:26 No.13332963 Report

Quoted By: >>13332971

>>13332541
???

Anonymous

Anonymous Mon 28 Jun 2021 02:06:27 No.13332966 Report

Quoted By:

>>13332875
learn calculus, teen

Anonymous

Anonymous Mon 28 Jun 2021 02:09:21 No.13332971 Report

Quoted By: >>13333213 >>13334496

>>13332963
Creating an irrational representation of rational numbers, or creating rational representations of irrational numbers.

Anonymous

Anonymous Mon 28 Jun 2021 03:31:11 No.13333213 Report

Quoted By:

>>13332971
it cannot be done. that's the whole point.

Anonymous

Anonymous Mon 28 Jun 2021 09:38:23 No.13334092 Report

Quoted By:

>>13332557
>approaches
0.999... is static, the amount of digits is inf from the get go
it's not a diesel engine chugging along
0.999... = 1

Anonymous

Anonymous Mon 28 Jun 2021 12:55:41 No.13334488 Report

Quoted By:

>>13332902
No

Anonymous

Anonymous Mon 28 Jun 2021 13:00:27 No.13334496 Report

Quoted By: >>13334513

>>13332971
Define what you mean by representation. If you mean "can be written as a sum of irrational numbers" then yes. If you mean that the rational is equal to some irrational number, then no and I suggest you luck up the exact definition of "rational number" and "irrational number"

Anonymous

Anonymous Mon 28 Jun 2021 13:09:51 No.13334513 Report

Quoted By: >>13334561

>>13334496
Yes written as was what I meant

Anonymous

Anonymous Mon 28 Jun 2021 13:32:36 No.13334561 Report

Quoted By:

>>13334513
Yes every number can be "written" as the sum of irrational numbers, but this isn't particularly impressive. For instance,
Let n be a rational number and let b = n + ?. Clearly b is irrational and n = b - ? so all rational have a so called "irrational representation". However, 0.999... is not irrational, nor is it an example of an "irrational representation".

Anonymous

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Anonymous Mon 28 Jun 2021 13:37:36 No.13334574 Report

Quoted By:

OP, read this. https://vixra.org/abs/2104.0141

Anonymous

Anonymous Mon 28 Jun 2021 15:35:46 No.13334803 Report

Quoted By:

>>13326157
It actually is only like 1-2 autist that debate it here per week or something. No post it in an actual normie place and watch the princely enjoyment you get from tards being tards.

Anonymous

Anonymous Mon 28 Jun 2021 16:04:30 No.13334871 Report

Quoted By:

>>13332557
0.999... doesn't approach anything

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