/sci/ - Science & Math » Thread #12079398

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Anonymous Thu 03 Sep 03:15:20 2020 No.12079398 View Reply Original Report

Quoted By: >>12079403 >>12079488 >>12079610 >>12079664 >>12079723

>browse this board as a high school senior brainlet
>see schizoposters schizoposting about Wildberger and reals don't reelz
>figure the definition must just be too complicated for these brainlets, hope I don't get filtered when I encounter it

>assigned Pugh in second-year analysis course
>get to the definition of reals
>literally the best and most intuitive definition fathomable
>realize /sci/ is just legitimately retarded

Anonymous

Anonymous Thu 03 Sep 2020 03:21:20 No.12079403 Report

Quoted By: >>12079419 >>12079623

>>12079398
Tookie talks about Dedekind cuts all the time, lurk more.

Anonymous

Anonymous Thu 03 Sep 2020 03:27:23 No.12079419 Report

Quoted By: >>12079425

>>12079403
Never uses them properly it would seem.

inb4 you're tooker and trying to be coy

Anonymous

Anonymous Thu 03 Sep 2020 03:32:44 No.12079425 Report

Quoted By:

>>12079419
When he comes he will ask me to not call him that.

Anonymous

Anonymous Thu 03 Sep 2020 04:07:54 No.12079488 Report

Quoted By: >>12079500

>>12079398
Can you tell me what textbook that is?

Anonymous

Anonymous Thu 03 Sep 2020 04:20:43 No.12079500 Report

Quoted By: >>12079503 >>12079508

>>12079488
anon says Pugh.

Anonymous

Anonymous Thu 03 Sep 2020 04:22:27 No.12079503 Report

Quoted By:

>>12079500
more like poo
LMAO
M
A
O

Anonymous

Anonymous Thu 03 Sep 2020 04:25:46 No.12079508 Report

Quoted By:

>>12079500
i am tired. thank you friend

Anonymous

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Anonymous Thu 03 Sep 2020 05:14:10 No.12079610 Report

Quoted By: >>12079615

>>12079398
Then address these problems.

Anonymous

Anonymous Thu 03 Sep 2020 05:16:29 No.12079615 Report

Quoted By:

>>12079610
if we wanted to be finitist bastards then one wouldn't really be talking about real numbers as there own whole, would we?

Anonymous

Anonymous Thu 03 Sep 2020 05:22:39 No.12079623 Report

Quoted By: >>12079638 >>12079678

>>12079403
No he doesn't lmao. He calls about "cuts" but he's no idea what they actually are in real analysis.

Anonymous

Anonymous Thu 03 Sep 2020 05:25:20 No.12079625 Report

Quoted By: >>12079633 >>12079634

I'm a physics phd trying to understand this because I never took advanced analysis
(and am a little drunk)
is this basically saying that you construct the reals by first taking the set of all rationals and then adding any numbers between and including the rationals? where the "cuts" are between two successive rationals?

Anonymous

Anonymous Thu 03 Sep 2020 05:32:15 No.12079633 Report

Quoted By: >>12079652

>>12079625
>set of all rationals and then adding any numbers between and including the rationals
No, that doesn't make any sense.
>where the "cuts" are between two successive rationals
No. There is no such thing as a successive rational. For any rationals q,p with q<p, q<q+p/2<p.
To understand cuts it's good to look at examples.
The number 2 is encoded in dedekind cuts as the set {q| q<2}.
How would you encode sqrt(2)? You just take {q| q^2 < 2 or q<0}. Any real number is encoded as the set of all rational numbers smaller than that real.

Anonymous

Anonymous Thu 03 Sep 2020 05:32:52 No.12079634 Report

Quoted By: >>12079636 >>12079652

>>12079625
There's no such thing as two "successive" rationals. What you want to imagine is A is the set of all the rational numbers below some real number which doesn't exist as a rational, and B as all the numbers above it.
The Cauchy sequence definition is more general and more instructive imo.

Anonymous

Anonymous Thu 03 Sep 2020 05:34:35 No.12079636 Report

Quoted By: >>12079702

>>12079634
>The Cauchy sequence definition is more general
How the fuck is it more general?

Anonymous

Anonymous Thu 03 Sep 2020 05:35:16 No.12079638 Report

Quoted By: >>12079639

>>12079623
Let's summon him then and ask him directly.

Anonymous

Anonymous Thu 03 Sep 2020 05:36:04 No.12079639 Report

Quoted By:

>>12079638
No need to. I've read his papers.

Anonymous

Anonymous Thu 03 Sep 2020 05:45:04 No.12079652 Report

Quoted By: >>12079656 >>12079663 >>12079665

>>12079633
I guess my confusion is then that the definition above for a cut involves two subsets. Yours seems to imply a single subset. For example, 2 is encoded as the set of all numbers less than 2(?)
And your sqrt(2) is encoded as the set of numbers q such that q^2<2 or q<0? I don't see what this says except that it gives an interval of numbers up to sqrt(2). I also don't understand the need for the 2nd condition q<0 since this allows for arbitrarily large negative numbers
>>12079634
so you're saying that the set of reals is defined by picking any number that can't be represented by a real number and taking every rational number below and above that. and then repeating this process for every other irrational number to construct the full set?

Anonymous

Anonymous Thu 03 Sep 2020 05:48:48 No.12079656 Report

Quoted By:

>>12079652
I mean "interval of numbers from -sqrt(2) to sqrt(2)"

Anonymous

Anonymous Thu 03 Sep 2020 05:52:03 No.12079663 Report

Quoted By:

>>12079652
also fuck
"any number that can't be represented by a RATIONAL number"
hopefully my ramblings are coherent to you guys, I appreciate this since there's not much tutoring for people like me

Anonymous

Anonymous Thu 03 Sep 2020 05:52:26 No.12079664 Report

Quoted By: >>12079670 >>12079711

>>12079398
d-do you think the posters on sci didnt know the definition of dedekind cuts?
we're the ones experienced enough to know that you cant teach a schizo the right things, so we never force feed them, cuz it doesnt fucking work
also
>muh intuition
never gonna make it you fucking brainlet

Anonymous

Anonymous Thu 03 Sep 2020 05:52:57 No.12079665 Report

Quoted By: >>12079674

>>12079652
>I guess my confusion is then that the definition above for a cut involves two subsets. Yours seems to imply a single subset.
The other subset is always the complement of the first, so you need only care about A.
> I don't see what this says except that it gives an interval of numbers up to sqrt(2).
sqrt(2) is not a rational number. You cannnot define a real number in terms of itself. You only have rational numbers to work with.
> I also don't understand the need for the 2nd condition q<0 since this allows for arbitrarily large negative numbers
Because, I am enlightened by my intelligence.
>>12079652
>so you're saying that the set of reals is defined by picking any number that can't be represented by a real number
Surely you mean represented by a rational number? And the process works just the same for all rational numbers.
>and taking every rational number below and above that
Yes, except that only makes sense once we've already constructed the reals. You can't define "all rational numbers below sqrt(2)" when sqrt(2) is not yet defined and that's what you're trying to do.

El Arcón

El Arcón Thu 03 Sep 2020 05:54:07 No.12079667 Report

Quoted By:

I used based Pugh in college.

Anonymous

Anonymous Thu 03 Sep 2020 05:57:01 No.12079670 Report

Quoted By: >>12079680

>>12079664
>>muh intuition
>never gonna make it you fucking brainlet
Don't listen to this guy, he doesn't know what he's talking about. Maths is all about intuition. Without intuition, maths would be simply manipulating meaningless formulas according to a predetermined set of rules. Nobody would find it interesting or enlightening. Intuition is what brings math to life.

Anonymous

Anonymous Thu 03 Sep 2020 05:59:17 No.12079674 Report

Quoted By:

>>12079665
>The other subset is always the complement of the first
okay I understand this
>sqrt(2) is not a rational number
okay, I was being hasty with my notation then, but what I meant was it gave the set of numbers q up to q^2<2. or is this also not true?
>Because, I am enlightened by my intelligence.
is this a meme or did you include this for a reason
>Surely you mean represented by a rational number?
yes I did sorry I added a correction because I'm retarded
>Yes, except that only makes sense once we've already constructed the reals
so it only makes sense once you've accounted for all the "cuts"? is that what I'm getting?

so if I were to attempt to reframe this myself, the reals would be constructed by all of the "cuts" which are comprised of numbers that cannot be constructed rationally and all of the rational numbers above and below these?

thanks for this, this is literally the first time I've seen this and am trying to understand this based on the OP image.

El Arcón

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El Arcón Thu 03 Sep 2020 06:01:22 No.12079678 Report

Quoted By:

>>12079623
I did devote a whole section to them in my paper. Section 7.5 is all about Dedekind cuts. IMO, it was one of the coolest things I did in the paper to make a distinction between the Cauchy sequence definition in Section 4 and the Dedekind cuts in Section 7.5. Usually people say they are pretty much the same but I showed they are pretty different.
[ Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis
https://vixra.org/abs/1906.0237 ]

Anonymous

Anonymous Thu 03 Sep 2020 06:01:52 No.12079680 Report

Quoted By: >>12079682

>>12079670
your entire reply is cope, you give no reason besides emotional appeals
why the fuck did you even post it

Anonymous

Anonymous Thu 03 Sep 2020 06:03:08 No.12079682 Report

Quoted By:

>>12079680
How much maths do you know? Like, what's the last topic you've studied?

El Arcón

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El Arcón Thu 03 Sep 2020 06:12:24 No.12079702 Report

Quoted By:

>>12079636
I also have a physics background and I agree with you. Anything other than $\mathbb{R}=(-\infty,\infty)$ is a circle jerk for doing physics.

Anonymous

Anonymous Thu 03 Sep 2020 06:17:44 No.12079711 Report

Quoted By:

>>12079664
>>muh intuition
Fuck off pseud, rigor is meant to enhance intuition not supplant it. In the end you're still left with intuition alone to define the "elements" of a "set."

Anonymous

Anonymous Thu 03 Sep 2020 06:22:34 No.12079723 Report

Quoted By:

>>12079398
What the fuck is this nerd shit, i've fled from biz in hopes of greener pastures but all i'm seeing are lemmings stufying how to cut a piece of string with scissors.

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