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/sci/ - Science & Math

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10272993 No.10272993 [Reply] [Original]

DEDEKIND CUTS ARE A FALLACY

>> No.10273012

calm down, Wildberger

>> No.10273024

Read spivak, m8.

>> No.10273195

>>10272993
chillax Cadet Capslock

>> No.10273259

>>10272993
What fallacy in particular, nigger?

>> No.10273329

*defines the reals as Cauchy sequences of rationals in your path*

>> No.10273385

>>10273259
educate yourself infinitist

https://www.youtube.com/watch?v=fXdFGbuAoF0
https://www.youtube.com/watch?v=jlnBo3APRlU

>> No.10273477

>>10273329
INFINITE SEQUENCES DONT EXIST

SHOW ME AN INFINITE SEQUENCE IN THE REAL WORLD MATH BOI

>> No.10273494

I'm a hyperreal chad and I hate every single one of you.

>> No.10273499

>>10273385
No fallacies there. Try again.

>> No.10273508

>>10273499
>didn't even watch the videos
shameful

>> No.10273521

>>10273508
I've seen them already. He never shows a fallacy.

>> No.10273535

>>10273521
>infinitist denial

>> No.10273556
File: 71 KB, 474x697, fake_numbers.png [View same] [iqdb] [saucenao] [google]
10273556

""""REAL""""

>> No.10273570

>>10273535
So just give me a quick rundown, one example of a fallacy. Hit me with your best shot.

>> No.10275170

>>10273477
just read the scales when yo' mama is standing on them

>> No.10275175

>>10273329
Advantages:
>easy to define sum and multiplication
>powers too
Contras:
>fucking equivalence classes
>I mean shit nigga miss me with that shit

>> No.10275180

>>10273477
>tying math to the real world
haha good one

>> No.10275190

>>10273329
cauchy is cooler than dedekind anyway

>> No.10275195
File: 2.79 MB, 853x480, pure math.webm [View same] [iqdb] [saucenao] [google]
10275195

>>10273477

>> No.10275209

>>10275190
>needing to mod out by equivalence classes because your definition is so arbitrary
fucking faggot

>> No.10275285

>>10275209
>the most intuitive definition that also works very well is somehow arbitrary
did someone forget to change your diaper or is your personality just always this bad?

>> No.10275312

>>10275285
>the most intuitive definition is initially arbitrary sequences of numbers which eventually have something to do with the thing we're defining then proving shit about equivalence classes because we were too dumb to think of a canonical structure
sounds like you're a brainlet who's conflating what's intuitive with what you were first taught

>> No.10275316

>>10273477
the infinite bang and crunch of the universe

>> No.10275394

>>10275312
>we're gonna have to do this gross shit so that we can get transcendentals
>why not just do that but for any non rational real number so we can just reduce the number of steps
you cant make a fucking structure that includes the transcendentals, thats why we went through this shit, the entire goal was to get completeness you moron

>> No.10275437

>>10275394
you take a set of shit less/greater than your number expressed as an algorithm and fill it in down/upward you fucktard. that's a canonical structure corresponding to any description of a trancendental.

>> No.10275448

>>10275312
A real number is an infinite sequence of digits modded out by 0.9999...=1. Prove me wrong, faggots

>> No.10275451

>>10273494
based and infinitesimalpilled

>> No.10275454

>>10275190
that's where you're wrong kiddo.
> complex analysis << algebraic number theory

>> No.10275456

>>10275195
Why are they white?

>> No.10275468

>>10273477
This is the problem with Wildberger. He never really shows anything wrong with infinite sets. He just appeals to a completely unrelated sense of something being able to exist in the real world. I can't make an infinite number of cuts in reality, but I probably couldn't count to a quadrillion either.

>> No.10275476

>>10275454
They're both faggots and I hate the diagonal argument it just seems so handwavey at first. Wildberger is right that real numbers are a meme, it's just that they're useful.

>> No.10275492

>>10275456
Only whites do math

>> No.10275498

>>10275456
asians hate themselves a lot. Its something we're not allowed to discuss unless its time to cast anime characters as blacks in a netflix adaptation in which case you can also cast whites as them while calling asians self hating for using white phenos in all their series.

>> No.10275505

>>10273385
This shit again.
As a solipsist I believe the highest number is around 7 or 8 as experimentally people generally can't hold that much more amount of things in their short term memory at one time.

>> No.10275516

>>10273329
This construction is way better pedagogically because there is an analogous one that allows you define Lebesgue integrable functions from sequences of Riemann integrable functions. It extends very naturally to discussions about function spaces, their completeness, how to do calculus on function spaces, spectra of linear operators, etc. See these notes if you are interested:

https://math.mit.edu/~rbm/18-102-S18/18-102-S18.html

The main difficulty is as these guys pointed out, having to deal with equivalent classes and modding out by sets of measure zero.

>>10275209
>>10275175

>> No.10277098

>>10273385
>Is a finitist.
>Can in theory do something useful or non-fallacious with math.
Pick only one.

>> No.10277327

>>10273024
Spivak is not about this, m[math]2^3[/math].

>> No.10277355

why care about reals when the universe is discrete?

>> No.10277657

>>10277355
kys quantumcuck