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Why is pre-university maths so focused on the Riemann Integral?

Anonymous Tue 05 Apr 19:06:34 2022 No.14367096 View Reply Original Report

Quoted By: >>14367103 >>14367106 >>14367260

Measure theory is arguably a lot more useful in modern applications and is completely left out in the average person's education.

Anonymous

Anonymous Tue 05 Apr 2022 19:10:41 No.14367103 Report

Quoted By: >>14367110 >>14367131 >>14367335

>>14367096
Measure theory is too abstract and crucially relies on infinitist schizophrenia, meanwhile the Riemann integral has a much clearer meaning and is much more applicable to the real world in terms of physics.

Anonymous

Anonymous Tue 05 Apr 2022 19:11:49 No.14367106 Report

Quoted By:

>>14367096
For me "pre University math" was just fucking around with equations. How do you teach Lebesgue integrations to students who have zero foundations in Analysis?

Anonymous

Anonymous Tue 05 Apr 2022 19:12:58 No.14367110 Report

Quoted By: >>14367185 >>14367187

>>14367103
Schitzo take. Both rely on infinitism in the same way.

Anonymous

Anonymous Tue 05 Apr 2022 19:18:59 No.14367131 Report

Quoted By: >>14367144 >>14367187

>>14367103
I understand the Riemann integral's importance in physics and it being the basis to understanding mathematics but measure theory is key to understanding statistics and probability theory which are more important for most non-STEM related disciplines.

Anonymous

Anonymous Tue 05 Apr 2022 19:23:02 No.14367144 Report

Quoted By: >>14367176

>>14367131
>measure theory is key to understanding statistics and probability theory
Its also key to understanding analysis, Riemann integration is basically irrelevant, since a superior theory exists. But obviously high schoolers (or equivalent) couldn't cope with it in any way.
We didn't even do *set theory*.

Anonymous

Anonymous Tue 05 Apr 2022 19:33:27 No.14367176 Report

Quoted By: >>14367193

>>14367144
>Riemann integration is basically irrelevant
Hence why I think someone who would not be able to understand set theory will never use basic analysis even once in their life and someone who pursues a career in STEM is faced with the limits of an older an inferior theory which they spent years on to perfect. Maybe I'm retarded but I feel like the systems not quite right.

Anonymous

Anonymous Tue 05 Apr 2022 19:37:18 No.14367185 Report

Quoted By: >>14367196

>>14367110
If you can compute maps of closed bounded intervals under your computable function then it's pretty obvious you can integrate your computable function over a closed bounded interval. No schizophrenia required.

On the other hand I personally don't know enough about this shit yet to know whether it's possible to do fancier integrals in a non-schizo way. There's probably some way to go further that what I said. Then again some of the functions people want to integrate are kind of schizo in and of themselves, like the Dirichlet function, as if you could compute such a thing.

Anonymous

Anonymous Tue 05 Apr 2022 19:38:10 No.14367187 Report

Quoted By: >>14367196

>>14367131
Infinitist statistics and probability is completely divorced from the real world and is basically devoid of any meaning. "Understanding" them amounts to understanding Manson's schizophrenic ramblings.
>>14367110
Incorrect. To take a riemann integral of a computable rational function, you merely have to take a limit of finite computations. That's one degree of (arithmetic) schizophrenia.
Meanwhile to compute the lebesgue integral, you need to talk about general measurable sets, which is already incredibly more complex because you're in the land of set theoretic schizophrenia now, way past arithmetic.

Anonymous

Anonymous Tue 05 Apr 2022 19:40:41 No.14367193 Report

Quoted By:

>>14367176
>someone who pursues a career in STEM is faced with the limits of an older an inferior theory
99% of highschool (or equivalent) math education is useless in university. Best case it gives you some intuition on the topic.

>Maybe I'm retarded but I feel like the systems not quite right.
High school math (or equivalent) is taught by 90 IQ "education majors", who's only qualification is symbol manipulation, teaching Zoomers with an attention span of one tiktok video.
I'm all for more advanced mathematical education, but clearly teaching Lebesgue integration won't happen.
I tutored first semester students, teaching them what a set is, before arriving at university, would be an enormous step in the right direction.

Anonymous

Anonymous Tue 05 Apr 2022 19:42:39 No.14367196 Report

Quoted By: >>14367215 >>14367233

>>14367185
>like the Dirichlet function, as if you could compute such a thing.
That's a measure.

>On the other hand I personally don't know enough about this shit yet to know whether it's possible to do fancier integrals in a non-schizo way.
Sums.

>>14367187
Either you accept real number theory or you don't.

Anonymous

Anonymous Tue 05 Apr 2022 19:48:21 No.14367215 Report

Quoted By: >>14367220

>>14367196
>real number theory
What theory? There is no theory. Just schizo ramblings.

Anonymous

Anonymous Tue 05 Apr 2022 19:50:39 No.14367220 Report

Quoted By: >>14367227

>>14367215
Real number theory is the best model of the continuum humans ever devised.

Funnily enough I recommended a CS friend of mine some Wildberger videos (lmao) and he promptly became an ultrafinitist...

Anonymous

Anonymous Tue 05 Apr 2022 19:52:37 No.14367227 Report

Quoted By: >>14367230

>>14367220
How is it a model of anything if you cannot even give a definition for what a real number is, nor how to determine what is or isn't a real number? This is math not social science.

Anonymous

Anonymous Tue 05 Apr 2022 19:54:20 No.14367230 Report

Quoted By: >>14367264

>>14367227
Boring. Talk about something else, do you have some anecdotes?

Anonymous

Anonymous Tue 05 Apr 2022 19:55:45 No.14367233 Report

Quoted By: >>14367242 >>14367247

>>14367196
What sort of sum do you have to do? Can you find converging upper and lower bounds for it?
Classically the Dirichlet function is certainly a function R -> R. Are you saying in a constructive setting it would be better implemented as a measure, or are you mixing it up with Dirac?

Anonymous

Anonymous Tue 05 Apr 2022 19:58:05 No.14367242 Report

Quoted By: >>14367247 >>14367249 >>14367257

>>14367233
>Classically the Dirichlet function is certainly a function R -> R. Are you saying in a constructive setting it would be better implemented as a measure, or are you mixing it up with Dirac?
I'm slightly drunk posting, the later.

>>14367233
>What sort of sum do you have to do?
Finite ones.

Anonymous

Anonymous Tue 05 Apr 2022 20:00:16 No.14367247 Report

Quoted By:

>>14367233
>>14367242
Also, did you know that the derivative of the Dirichlet function (as a measure, evaluated on R^n) of a set is its Perimeter? (Or at least a very good definition of such).

Anonymous

Anonymous Tue 05 Apr 2022 20:01:08 No.14367249 Report

Quoted By: >>14367259

>>14367242
>Finite ones.
Coming from the mouth of an infinitist, that's utterly meaningless.
The infinitist will swear on his mother's grave that {1 if CH is true and 0 if CH is false} is a natural number just like 1,2,3.

Anonymous

Anonymous Tue 05 Apr 2022 20:03:50 No.14367257 Report

Quoted By: >>14367262

>>14367242
>Finite ones.
But then do you have to take limits / supremums of those sums to get the integral? That's where classical constructs often derail into uncomputable land.

Anonymous

Anonymous Tue 05 Apr 2022 20:05:09 No.14367259 Report

Quoted By:

>>14367249
How does finitist integration theory look like?

Did you know that computers can produce correct results for very many objects in standard analysis. (Without computer algebra).

Anonymous

Anonymous Tue 05 Apr 2022 20:05:31 No.14367260 Report

Quoted By: >>14367263

>>14367096
This is exactly the problem with mathfags.
Yes, measure theory is the foundation of modern analysis and having some working knowledge of its methods and ideas is a fundamental part of any aspiring pure or applied mathematician.
However, its nonsensical to teach this to students from non math disciplines that really only care about applications where the mathematics are seldom the problem.
Additionally, its completely crazy to try to teach measure theory to laymen during highschool.

Anonymous

Anonymous Tue 05 Apr 2022 20:08:03 No.14367262 Report

Quoted By:

>>14367257
>That's where classical constructs often derail into uncomputable land.
funnily enough they don't.
It is possible, given some "reasonable" function, for a computer to calculate *correct* upper and lower bounds of an integral *only using approximate floating point numbers*.

Also the joke was that finitists would use finite sums as integrals...

Anonymous

Anonymous Tue 05 Apr 2022 20:09:28 No.14367263 Report

Quoted By:

>>14367260
>Additionally, its completely crazy to try to teach measure theory to laymen during highschool.
It should be taught to a select group of students. But the modern western school system, in all its aspects, is very much set against individual excellence.

Anonymous

Anonymous Tue 05 Apr 2022 20:09:32 No.14367264 Report

Quoted By: >>14367266 >>14367284

>>14367230
One time I found a real number so astounding, so unbelievable, that I had to check twice that it's actually there. Do you want to guess what the number is? You can ask me questions about it, yes or no questions and I will answer you.

Anonymous

Anonymous Tue 05 Apr 2022 20:10:29 No.14367266 Report

Quoted By: >>14367271

>>14367264
>You can ask me questions about it, yes or no questions and I will answer you.
Was she cute?

Anonymous

Anonymous Tue 05 Apr 2022 20:12:49 No.14367271 Report

Quoted By: >>14367279

>>14367266
I don't like your questions. Go coom then come back.

Anonymous

Anonymous Tue 05 Apr 2022 20:15:22 No.14367279 Report

Quoted By: >>14367280

>>14367271
You said you will answer me if I ask a yes/no question.
I asked a yes/no question, but you didn't answer.

Also, masturbation is a sin, so I won't heed your "advice". The question still stands.

Anonymous

Anonymous Tue 05 Apr 2022 20:16:21 No.14367280 Report

Quoted By: >>14367283

>>14367279
No

Anonymous

Anonymous Tue 05 Apr 2022 20:19:04 No.14367283 Report

Quoted By:

>>14367280
>NO DON'T ASK ME THESE QUESTIONS ABOUT MY NUMBER
Cope harder finitist.

My x, where x is a non computable real number, is heckin real and heckin valid, just as much as 2 is.

Anonymous

Anonymous Tue 05 Apr 2022 20:19:42 No.14367284 Report

Quoted By: >>14367300

>>14367264
Is it computable?

Anonymous

Anonymous Tue 05 Apr 2022 20:33:31 No.14367300 Report

Quoted By: >>14367315 >>14367316

>>14367284
No

Anonymous

Anonymous Tue 05 Apr 2022 20:37:32 No.14367315 Report

Quoted By: >>14367330

>>14367300
If you had an oracle that output its digits, could you use it to solve the halting problem?

Anonymous

Anonymous Tue 05 Apr 2022 20:37:46 No.14367316 Report

Quoted By: >>14367330

>>14367300
Would you say the number is rather "red", like 3, 7, 18.5588242 or rather "blue" like 19.5, 2, 5678?

Anonymous

Anonymous Tue 05 Apr 2022 20:43:31 No.14367330 Report

Quoted By: >>14367338

>>14367316
Yes.
>>14367315
No.

Anonymous

Anonymous Tue 05 Apr 2022 20:45:22 No.14367335 Report

Quoted By: >>14367339 >>14367352

>>14367103
The Riemann integral does also rely on infinite processes and in the case of the equivalent darboux definition involves calculating suprema and infima of sets (whose existence relies on properties of the real numbers). If you don't like infinities then analysis in general is out of the question

Anonymous

Anonymous Tue 05 Apr 2022 20:47:00 No.14367338 Report

Quoted By: >>14367355

>>14367330
If I asked you whether its digit (base 10) number 2574327863786438953588 was 0, would you just make a random choice?

Anonymous

Anonymous Tue 05 Apr 2022 20:48:09 No.14367339 Report

Quoted By:

>>14367335
He obviously is either trolling of has no clue about mathematics, e.g. edgy undergrad.

Anonymous

Anonymous Tue 05 Apr 2022 20:53:49 No.14367352 Report

Quoted By:

>>14367335
Bishop exists. Then again a quick search shows people working on constructive measure theory.

Anonymous

Anonymous Tue 05 Apr 2022 20:54:51 No.14367355 Report

Quoted By: >>14367368

>>14367338
No. Nothing in this world is random.

Anonymous

Anonymous Tue 05 Apr 2022 20:59:36 No.14367368 Report

Quoted By:

>>14367355
>Nothing in this world is random.
QM BTFOed.
I thought you finitists loved QM because it "showed" that the universe is discrete?

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