Logic - 2017-12-08 (page 2 of 3)

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7:07 AM

@DavidReed Well if it uses an ultrafilter, that is where the problem lies. You see, the uncountability of the reals is a red-herring, because there is a countable model of any first-order theory, including MS, as long as it is consistent.

I'm perfectly willing to look into that also. It was more thinks that were going on the formal logic side of the construction that was raising my eye.

I'd like to hear your version of the hyperreals anyway.

Since you say it uses an ultrafilter, but the typical use of that is to get the ultraproduct, in this case ultrapower.

But you say yours doesn't do that.

And yet not by compactness, which is the other way I know to get a hyperreal field.

Ah yes, its a "lets first do this my way, and then we'll do it everybody elses way in the next chapter part of the book type of setup

Are you able to sketch it?

but yes putting a measure on the ultrafilter gives it the construction of the field, the transfer properties that let us automatically know that effectively everything true in the reals will be true in the hyperreals is the part that's throwing me

its an ancient text

If you'd like I can set you up as an authorized reader on my kindle acct. I have something like 200 textbooks on there from all arenas of academmia

that book included

7:17 AM

The transfer principle is obvious in the ultrapower construction, and the ultrapower construction is immediate from the existence of an ultrafilter. Though you say your book does not use the ultrapower, but you mention using the ultrafilter to get a measure, and that sounds very much like the ultrapower construction...

How about you take a look at Rautenberg and tell me whether it's essentially the same idea?

It's linked from "Good intro texts for logic" on the right.

@DavidReed Thanks, but I don't have a kindle, and am quite paranoid about installing things.

you don't have to

you can access it directly from amazon's website. Called kindle cloud reader

it is a pantheon of all areas of academia. I'm sure you could find something in there you'd enjoy

No installation either

Hmm, if I ever need something from there, can I ask you again? I'm really more paranoid than you might suspect; all Javascript is disabled by default except on sites I trust, and even then some Javascript is still not enabled.

Let me see if I can compile the title list here for you

Thanks again.

You do strike me as paranoid

I'm trying to find a way to just get the titles w/o the graphics

7:25 AM

(I got infected once by a malware, and decided that that was enough.)

ok. off the top of your head, pick a topic

Um... 3-valued logic.

kindles down, I have 3 logic books in there and it wont let me view the toc

Really, never mind about that.

But now we might as well settle your question first. Given an ultrafilter F on ω, you just define R^ω to be the set of sequences from R, and then define the functions pointwise, and define the predicates to hold according to F.

R is the reals.

ω is the naturals.

Namely, given predicate P (whatever you like on reals, say ordering) and sequences x,...,y from R, define P(x,...,y) to be true iff { k : k∈ω ∧ P(x[k],...,y[k]) is true } ∈ F, and false otherwise.

Finally define equality on R^ω as if "=" is a predicate-symbol.

Then let R* = R^ω modulo that equality.

Now the ultrafilter properties come in when you want to show that every true sentence about R is true about R*.

Which is the transfer principle you seek.

let me pull this text up so i can parallel your construction

hold up

7:37 AM

The way in which the ultrafilter properties are used is really the same as the fact that it induces a finitely-additive measure on subsets of ω. R* is called an ultrapower of R.

Ok I'm going to withdrawal my objection to his approach at this time, even though I don't like it

In the application here, one only needs a finite number of symbols to name real numbers at a time, as opposed to having to have a name for all of them simultaenously

you really enjoy teaching I've noticed

@user21820 you still there man?

@DavidReed I'm still here. Just didn't notice your messages as I was doing something else in parallel.

Ah ok

@DavidReed I do (enjoy teaching).

But as I said before, while I understand how to do this stuff (hyperreal construction), I don't buy it, since I don't believe transfinite induction up to ω[1].

I'm typing up this sub(s,c,d) thing for leaky nun

7:50 AM

Sure! He'd love it.

hopefully it'll stay posted long enough for people in CRUDE not to flip.

Do you ever feel that you're more excited teaching someone than they are to learn it?

@DavidReed Oh you mean posting on Main? Well as long as it shows effort and is not cranky, I like it. Other people might not, but that's their problem.

what does cranky mean?

Means like proving the Collatz conjecture or Fermat's Last Theorem or something like that in one page.

Or worse still, proving that PA is inconsistent.

@DavidReed That's usually the case. But I also try to avoid teaching people who do not actually want to learn. As you can probably tell, my style of teaching will put off those who want quick answers without understanding.

did you see the one yesterday where someone claimed the naturals were uncountable, proving it via some weird diagonal argument, and then said he had resolved the continuum hypothesis

7:54 AM

@DavidReed Nope. Please post links to such nonsense in CRUDE so that we can get onto them.

(Or I might have seen it and already acted on it but forgot; there are too many of them.)

i think they did, somebody only posted it because someone had said "no action necessary when reviewing it

you would remember..trust me

Oh Asaf did.

I do remember.

math.stackexchange.com/review/late-answers/918155

I can't read it without laughing

absurd is an understatement

I have learnt to evaluate crankiness quickly. I took one glance at it and it was enough; so I didn't even get to laugh hahaha..

oops

The above demonstration has some interesting implications regarding the Continuum Hypothesis. I have demonstrated the Natural Numbers are not countable and the fact that the Real Numbers on the (0, 1) interval are equally not countable means that both sets possess the same cardinal number. As a consequence of this fact that there can be no infinite set with a cardinal number between them. The Continuum Hypothesis is true because the naturals and reals have the same cardinal number.


oops

there

8:02 AM

If you copy and paste text with at least one line-break, you will be able to post the whole lot (as long as not too big). That's how you can post programs in here. If on the other hand you want to post just the link, you can click on "share".

@DavidReed hi

hey man

Oh I forgot you don't have 10k rep and can't see the deleted post.

(Except in the review queue.)

but yah just the last paragraph there. I don't know how to react except laugh

@DavidReed It's literally begging the question, even if it's true that the naturals are uncountable.

8:15 AM

Letting $quo(x,y)$ be$ x/y$, $lh(s)$ defined to be the length of the sequence,

$ent(s,i)$ the ith member of the sequence coded for by S

$\pi(n)$ the nth prime counting 2 as the $0th$

$$
sub(s,c,d,0):=
\begin{cases}
s & \quad ,fst(s)\neq c\\
\\
qou\left(s,3^c\right)3^d & \quad ,fst(s) = c \\
\end{cases}
$$

$ \\ $

$$
sub(s,c,d,i')=
\begin{cases}
sub(s,c,d,i) & \quad ent(s,i)\neq c \\
\\
quo\bigg(sub(s,c,d,i),\pi(i+1)^c\bigg)\pi(i+1)^d & \quad ent(s,i) = c
\end{cases}
$$

Then $$sub(s,c,d):=sub(s,c,d,lh(s))$$

@LeakyNun there it is my friend

@LeakyNun you there?

@user21820 You up?

@DavidReed Yes. I thought it's time for you to sleep?

Its definitely getting to that point

Better go. Rest well!

bummed i typed this up for nothing

have a good night man

@DavidReed He will surely reply when he's here next time.

And same for me; if I'm not around I'll reply the next time.

Good night!

4 hours later…

12:10 PM

@user170039 I've read through this one, and I do not see any concrete justification for its claims. As I said earlier, the axiom of reducibility nullifies the philosophical justification of the soundness of the type hierarchy, and the article does nothing to repair this.

@user170039 This one makes me even more confident that there is little to be gained by attempting to figure out what Russell's final views were on his type theory. I'd rather just look at properly described systems. However, it makes an interesting point about λ-calculus on pages 223−224, that it is unsatisfactory that the λ-abstraction seems to be an individual object in itself but yet cannot be applied to itself.

Indeed, that is why I am unsatisfied with any system (be it set theory or type theory) that claims to be foundational but does not have a universal type.

@user21820 I haven't read through this myself, but mentioned the other day. It was put together "on accident" at a seminar at princetons institute for advanced study.

@DavidReed What are you referring to?

homotopytypetheory.org/book

They just decided it was possible in the last 3 yrs

its free pdf

Ironically I found it the same day I was engaged in heated discussion with comp sci person that there was no way lambda calculus could ever replace FOL as a foundatioinal system for math

3

A: What is the benefit in constructing the integers from natural numbers?

The result comes from a strong historical desire to find a list of axioms from which all mathematical truths could be proved in a first-order system. With the advent of calculus, people began to prove all types of completely incorrect statements by their cavalier manipulation of the infinite. Thi...

12:26 PM

@DavidReed Well as I stated in the comment before yours, I am unsatisfied with any proposed foundational system that does not have the universal type.

@user21820 Does it declare not to have one?

HoTT has ω many universes, and no final one for exactly the same reason that ZFC cannot have a set of all sets.

are you familiar with this principle of univalence?

@user21820 when using the @handle will it send to the user in another chatroom?

@DavidReed No it only applies to the chat-room you use it in. When you press @ you can see all the users that are pingable in that chat-room. Users who have not visited for a while will become no longer pingable there.

@user21820 I see two persons pingable that aren't in the chatroom

@user21820 Given your passion on the topic : math.stackexchange.com/questions/2557068/…

12:43 PM

@DavidReed I have looked at it and disliked it. Informally it says that any two isomorphic structures are identical.

@DavidReed They don't have to be present. The "while" is "2 weeks if I recall correctly.

For instance on page 75 of the book you linked, it says "Note that a homotopy is not the same as an identification ( f = g ) . However, in §2.9 we will introduce an axiom making homotopies and identifications “equivalent”."

There is no philosophical reason for doing so, and arguably it's philosophically unsound.

@user21820 That perspective on isomorphism was killed for me when I discovered a field could be isomorphic to one of its proper subfields.

Wait what?

?

What is such a field?

I believe I found that on this site

hold up

Yes, given any field k
k
, k(x)
k(x)
is isomorphic to k(x 2 )
k(x2)
.

2

Q: Fields and proper subfields.

Specific question: Let $F$ be a field and assume that $\mathbb{Q}$ is a proper subfield of $F$. Can $F$ be isomorphic to $\mathbb{Q}$? Studying the foundaments of field theory I have to ask: Can a field be isomorphic to one of its proper subfields?

field-theory extension-field class-field-theory

12:51 PM

Hmm well this example of F(x) ~= F(x^2) for transcendental x over F is obvious. I forgot it. But AlgClosure(C(x)) ~= C is harder to intuitively grasp for me.

Even though I know the proof...

Anyway, proponents of 'that perspective on isomorphism' can argue that this does not furnish a counter-example, in the sense that a priori it is possible for something to be a strict substructure of itself.

Consider that (Q,<) ~= ((0,1),<) as linear orders.

My rejection of that perspective is simply because there is no reason for it to be true.

My perspective is that one should simply be cautious calling non-indentical things the same

That's the same reason, isn't it?

lol

No unjustified assumptions?

One of the most frustrating times I had in alg was when you show every polynomial over a field has an extension containing a root. Of course it wasn't an extension, it was an embedding into a completely disjoint field

12:59 PM

@DavidReed You could afterward find a true extension simply by replacing the embedded field with the original and modifying the operations accordingly.

Finally I went through and pulled out the subfield and defined all the ops.

yes that's what i did

The only thing is that this only works finitely many times. You can't do it infinitely many times without a lot more technical care.

I've seen many wrong proofs of the existence of algebraic closure via Zorn's lemma in ZFC, too.

didn't seem to bother anyone else in the class that we had just jumped into an entirely disjoint set

I specifically avoided passing to a normal closure when doing gal proof of the fundamental theorem of algebra

@DavidReed Lol. Nothing bothers anyone when they aren't actually concerned with the soundness of their deductions.

Basically one shows that it suffices to prove it for some real poly f, then you set

set$ g = (x^2+1)f$ and you're guarenteend to have C be an intermediate field

@user21820 outside of logic, what areas o math/academia interest you.

1:09 PM

@DavidReed I like useful and elegant stuff. You could see my profile on Math SE for links to some stuff I find nice.

the useful stuff is so rarely elegant

do you collect elegant proofs?

Haha.. I don't collect per se, but I tend to recall the main ideas so that I can reproduce them.

That's the secret man. Remember the trick

Have you seen zolotarev's quadratic reciprocity proof?

Nope; I'm not so into number theory so my knowledge stops somewhere before quadratic reciprocity.

Well if you haven't I spent three hours typing it up to share with people here, was a self-ask self-answer and came very close to being deleted because I "put more effort into answering my question then the question itself"

It would be trivial for you

2

Q: Zolotarev's Lemma and Quadratic Reciprocity

The law of quadratic reciprocity is unquestionably one of the most famous results of mathematics. Carl Gauss, often called the "Prince of Mathematicians", referred to it as "The Golden Theorem". He published six proofs of it in his lifetime. To date over 200 proofs of this result have been found....

number-theory quadratic-reciprocity

Going into it all that one needs to know is that $a^{p-1/2} = 1$ iff a is a square mod p

1:17 PM

I googled and found mattbaker.blog/2013/07/03/…, which looks like a nicely illustrated version haha.. Will read both when I've the time.

blech. He's going to make you count transpositions in a really unnatural ordering

The one I put up was compiled from a number of sources. I wrote it to be dummy proof so that's the only reason its as long as it is.

@DavidReed Haha okay.

Make sure to upvote it while you're there. The Italian insisted I make it a community wiki, so no rep benefits

Which Italian? The mod?

After i hit 2k I don't think I'll care anymore

yes

"This is something I've never seen before, a beautiful self answer to a horrific self question. What is the reason for this behavior"

1:22 PM

That's wrong; there is no rule or community consensus that self-answered posts should be CW, and in fact it is the contrary.

He just said it would be best, I already had two close votes on it. Did what was necessary to avoid having lost 4 hrs of my day.

I guess you're facing pretty much the same kind of jokers who spited my post on the incompleteness theorems. They downvoted both my question and my answer, and spewed junk comments on my question instead of insightful comments. I got a moderator (quid) to help curtail the junk, and I left just one of my comments:

For reference, good quality self-answered questions are actively encouraged by both the StackExchange guidelines as well as a current moderator and a past moderator. — user21820 Oct 24 at 6:32

You can take note of these links if you need them in the future.

Anyway I'll read your post later; got stuff to do now.

See you!

user131753

2:05 PM

@user21820 Why exactly?

> I'd rather just look at properly described systems.

user131753

@user21820 Then it is your personal choice.

Give me a precisely described system and its purpose (whether it's supposed to be foundational or not) and we can talk. I'm not interested in what X says Y meant when Y said/wrote Z at time T, especially when Y is no longer alive.

user131753

@user21820 I think it mainly depends on what you consider to be an "philosophical justification" of an axiom. What is "concrete justification"?

@user170039 It's up to you to decide on that and convince me, if you wish to justify something.

Strictly speaking, I'm most interested if you can justify that something is meaningful and sound for the real world.

user131753

2:12 PM

@user21820 I don't think so. You used the terms and I think that the burden of explanation is upon you.

@user170039 Then we stop here. I've adequately explained what I meant to you a couple of times, but each time you brush my explanations aside. I'm not interested in hearing about other people's ideas when they are so poorly explained/written.

If you (conveniently?) forgot my explanations, please read the following post as well as Terence Tao's answer, which shows that he not only grasps my notion of real world meaning, but also more or less affirms my view.

48

Q: Physical meaning of the Lebesgue measure

Question (informal) Is there an empirically verifiable scientific experiment that can empirically confirm that the Lebesgue measure has physical meaning beyond what can be obtained using just the Jordan measure? Specifically, is there a Jordan non-measurable but Lebesgue-measurable subset of ...

mp.mathematical-physics lebesgue-measure

lol

wow

Wow what? In case it's unclear, I'm referring to the articles that @user170039 linked as poorly explained/written.

user131753

@user21820 From a metaphysical point of view, I don't even know what exactly is the real world much less what is meaningful and sound for. Anyway, I also think that pursuing this discussion further is going to be waste of time. So let's stop here. Also while it is true that you have explained what you meant by "philosophical justification", if you remember, I don't think I have ever agreed with your explanation .

Just came back here and noticed the tension

2:20 PM

@user170039 It's fine if you disagree. I have no problems with that. I have problems with you saying that I haven't explained my terms...

physical meaning of the lebesgue measure

for me its the least amount of tape you need to cover up a set on the line

@DavidReed That notion gives a very low-complexity definition of measure.

It doesn't give full countable additivity.

it was a joke

I thought you were serious.

Because it's like open covering.

Although, If I had to explain to a layman what the measure of a set on the real line would be that would be my approach

2:24 PM

Well if your tape has open boundaries, and you have countably many fingers, you can argue that it's okay.

yes an infinite amount of tape, that can be cut in very jagged ways

But seriously, there are philosophical issues with countable stuff embedded in different structures available in ZFC.

As I stated in one of the comments in that MO thread:

To clarify, the collection of halting programs is a well-defined notion but may not have a physical meaning if you embed it into say lattice points in space. We're so used to embeddings meaning "essentially the same" that we easily assume that physical meaningfulness is preserved under embeddings. It isn't, unless the ambient structure supporting our embedding is itself physically meaningful! For example, the physical meaningfulness of the collection of rational numbers encoded as strings is witnessed by the program that accepts it, but not as a subset of the ordered reals or so I think. — user21820 May 9 '16 at 9:48

It is related to the Lebesgue measure in the sense that we can prove the rationals have zero measure, but actually they don't have zero Jordan outer measure, which is why in practice we will never be able to cover the rationals with zero tape...

user131753

@user21820 You didn't explain this term, i.e., "philosophical justification" (a simple room search reveals that). Even on an earlier occasion (so far as I can remember) you gave an example of what you don't consider as a "philosophical justification".

@user170039 A simple search of your own room reveals that just recently I had given an explanation of that.......

in Philosophy of Mathematics, Sep 11 at 13:25, by user21820

@user170039 In my linked post I explicitly cited Boolos, who said the same thing as I did in my answer. Originally I just posted my answer based on direct logical analysis of the claimed ontological justification for replacement as some people have given, and explained why it was circular. However, it seemed clear that a couple of readers did not have the logical facility to understand the circularity, and I happened to later find about the part I quoted from Boolos.

And the subsequent comments.

In particular:

in Philosophy of Mathematics, Sep 11 at 13:29, by user21820

@user170039 The problem is that we can see and explain clearly what is circular, but we cannot necessarily tell you what a reasonable ontological justification might be. Perhaps there is one that we have yet to think of. But up till now no logician has seemed to have done it.

user131753

@user21820 Was it supposed to be an explanation rather than just giving a vague idea of the term of of the problem associated with the term?

2:36 PM

It was supposed to emphasize that I am not insistent on a particular form of justification that I would accept, and no others.

I leave it up to anyone (including you) to decide what is the most convincing kind of justification you want to present.

And your only goal is to convince me that it is somehow meaningful to the real world.

user131753

24 mins ago, by user 170039

@user21820 I don't think so. You used the terms and I think that the burden of explanation is upon you.

user131753

Anyway, let's stop here. This discussion is being pointless.

Please define "pointless".

That is the kind of definition you're asking me to give.

I'm trying to tell you that the most I will give is the one I gave in the MO post, since I do not want to arbitrarily restrict the discussion to be in my favour!

I could easily say that I only consider things to be justifiable if it can be interpreted in higher order arithmetic, and then automatically ZFC is not justifiable. But that is simply not fair to anyone who wishes to discuss the topic.

@DavidReed It's always like this. In my opinion people should not attempt to talk philosophy of mathematics without already having a thorough grasp of first-order logic, the incompleteness theorems, and computability theory.

Unfortunately, most philosophers I've seen know practically no logic, and hence make all kinds of silly statements. Some say that Godel's results are flawed or meaningless or can be circumvented or whatever...

Sry just got back

was explaining to physics undergrad having nervous breakdown the difference between differentials and limits

Lol.

What did you say?

2:50 PM

Well, initially I made a comment about how I hated physicists for being awful mathematicians, and I was really making it more to the people that were answering his question. Then he said to me:

flag

@DavidReed This is exactly the problem I face. Studying physics and mathematics simultaneously has let me conclude that dydx
dydx
is a fraction, but only so in limited number of cases. Its very confusing when on one hand you're told that dydx
dydx
is a fraction of infinitesimals, but on the other hand we're told that ddx
ddx
is an 'operator'. So convenient. – YourAverageEuler 36 mins ago

So i made a post

0

A: Is there a difference between $\frac{|{\mathrm{d}y}|}{\mathrm{d}x}$ and $\biggr|\frac{\mathrm{d}y}{\mathrm{d}x}\biggr|$?

In response to your comment. Calculus was historically formulated in terms of infinitesimals. That is numbers that are infinitely small, that is where this notation, due to liebnitz, hails from. The truth of the matter is there are no infinitely small real numbers. It's possible to create an ext...

user131753

@user21820 And why exactly is that?

The reason is given in my next comment.

That's exactly why I'm not so interested in many philosophers' writings.

I understand you're interested, but sorry not my cup of tea/coffee.

user131753

@user21820 I think we had a discussion regarding this. Probably back then you mentioned Wittgenstein, right?

Nope, you did. I wasn't the one who brought him up.

user131753

Oct 9 at 16:24, by user 170039

@user21820 Do you have any particular non-logician in mind to whom these remarks apply?

user131753

2:54 PM

Oct 9 at 16:26, by user21820

Haha we've been over this before; Wittgenstein is one. I've not seen him write any logically clear argument about mathematical logic. So there's really nothing much to say; everyone can interpret him however they wish but he alone knows for sure whether he really knows what he's talking about.

I may have recalled the wrong person then, though I was quite sure you first mentioned one of his writings.

Before that exchange.

If not, then it could be this other person:

Jan 4 at 5:59, by Harry

Though, like you, I have more "risky" side projects. Philosophical logic and Wittgenstein interests me the most. But I figured a computational logic masters would be fairly well received...if I manage to succeed

what is this about btw>

What is the party with the burden of persuasion trying to get across

It is about who brought Wittgenstein up first.

I'm trying to understand how that could be worth 30 min of debate

@DavidReed I am trying to get across that I have no need of any burden. I'm not the one preaching my views to @user170039, who is usually the one telling me that this/that article might be interesting, and (it seems) getting upset when I say I don't buy them.

2:59 PM

what article?

3 hours ago, by user21820

@user170039 I've read through this one, and I do not see any concrete justification for its claims. As I said earlier, the axiom of reducibility nullifies the philosophical justification of the soundness of the type hierarchy, and the article does nothing to repair this.

3 hours ago, by user21820

@user170039 This one makes me even more confident that there is little to be gained by attempting to figure out what Russell's final views were on his type theory. I'd rather just look at properly described systems. However, it makes an interesting point about λ-calculus on pages 223−224, that it is unsatisfactory that the λ-abstraction seems to be an individual object in itself but yet cannot be applied to itself.

If you're so interested, click to follow the links to what I was replying to.

user131753

@user21820 Anyway, the point I am willing to stress is that although studying mathematical logic is extremely helpful philosophy of mathematics, it is not correct to say what you wrote here. Your remark would be very much applicable for "foundations of mathematics" but not for "philosophy of mathematics" as a whole.

@user170039 I'm interested in foundations of mathematics. I'm not interested in mathematics that does not seem relevant to the real world, though I still learn ZFC to know how modern mathematicians think. Does that explain everything to you now?

I'm likewise not interested in philosophies that are immoral or irrelevant to the real world.

@user170039 homotopytypetheory.org/book

free download, read at your convenience

were you the one discussing symbols with me yesterday?

@DavidReed Wasn't it me?

Or LeakyNun.

3:04 PM

No someone going on about infinite knowledge energy machine or something like that

That was user76284.

ah

user131753

@user21820 Then you should have been more precise about that from the beginning. I though that you are genuinely interested in philosophy of mathematics. Sorry about that.

user131753

@DavidReed: Did you give me the link of the book for any particular reason?

@user170039 "Philosophy of mathematics" has never been precisely defined, not by you or by anyone else. In my own definition, true philosophy of mathematics only comprises philosophy pertaining to mathematics that is relevant to the real world.

Of course, you're free to disagree, as many philosophers do.

3:07 PM

I did

I saw you talking about types

this is something they're doing at Princeton in terms of finding a new foundation for mathematics in type theory instead of FOL

I thought you might find it an interesting read. They're distributing it freely from that website

user131753

@DavidReed: Oh. I see. Thanks for the link.

user131753

@DavidReed: You are welcome to this room if you want to discuss anything about philosophy of mathematics.

Excellent. Thank you for the invitation.

Do you consider this to be a bad post?

user131753

@DavidReed: Was it addressed to me?

both of you really

3:15 PM

→ 1 message moved to trash

Sorry something went wrong.

Please repost it.

........

→ 2 messages moved to trash

It says you just invited me to join the trash

That's a side-effect of moving any message that pings you. You can ignore it.

So did something go wrong? Or were you being intentionally nonsubtle regarding your opinion of what I told him

3:17 PM

@DavidReed I responded to your message that implied I wasn't willing to listen, but you didn't respond, so I deleted both.

Somehow, the system deleted your most recent message instead.

I didn't suggest you weren't willing to listen

Although phrases like "Unless it has universal types I'm not interested in it" will give people that impression

You said "the harder you push someone to engage in that way the firmer they dig in their heels" implies that it is the way user170039 was pushing me to engage, thus implying I was unwilling to listen.

Of course I agree about the pushing and about the digging in heels, but not about the "unwilling" part.

Yes, most definitely within the context of the last 20 min You've been unwilling to listen, but I meant that as a result of having someone try to convince you of something that lost your interest a long time ago

Fine. I admit that. But note that I spent an hour or two on those two articles he linked me to, before I made my judgement.

I did not summarily dismiss them.

Mainly I was reacting to the immense amount of noise that seemed to be going nowhere

I understand

3:22 PM

Agreed.

Let's get back to logic.

@DavidReed: You mentioned this post:

1

A: Is there a difference between $\frac{|{\mathrm{d}y}|}{\mathrm{d}x}$ and $\biggr|\frac{\mathrm{d}y}{\mathrm{d}x}\biggr|$?

In response to your comment. Calculus was historically formulated in terms of infinitesimals. That is numbers that are infinitely small, that is where this notation, due to liebnitz, hails from. The truth of the matter is there are no infinitely small real numbers. It's possible to create an ext...

Hes he upvoted it

Can I invite him in here

As I said before, the hyperreals are useful only after one accepts the meaningfulness of ZFC, otherwise it's unclear that you will prove meaningful results using them. In fact, one does not need infinitesimals at all to get intuitive explanations of real analysis.

@DavidReed Yes by all means.

As linked from my profile, see this post:

4

A: When is the derivative of an inverse function equal to the reciprocal of the derivative?

The answers so far are not correct; they merely give sufficient but not necessary conditions, yet some of them state that their conditions are necessary. You do not need differentiability in some neighbourhood of the point. You do not even need one-to-one correspondence between the values of $x$ ...

hence the part "not much is gained from it"

@DavidReed Exactly I understood that part.

user131753

@user21820 Can I provide @DavidReed the link of the extensive discussion between you and Mikhail Katz regarding this issue?

3:27 PM

@DavidReed: You will see that by considering asymptotic classes instead of mere values, you can recover all the intuitive analysis reasonings.

Simply Beautiful Art

Conversation may be suitable for Constructive Feedback.

@SimplyBeautifulArt Uh what?

Simply Beautiful Art

Idk, seemed like you guys were discussing the validity of something

@user170039 You may, but I'll say that that person is stubborn and very controversial on this site, even among ordinary mathematicians.

Simply Beautiful Art

:-/ maybe constructive feedback isn't suitable. Ignore me.

3:29 PM

@SimplyBeautifulArt Oh well yes he's getting feedback on his post, but I don't think in the same sense Constructive Feedback room was intended?

I thought it was for asking how to improve (site-wise) one's post.

my post?

Simply Beautiful Art

*Shrugs*

what controversial person are you talking about?

@DavidReed: A moderator once told me that that user is "known to email fellow members of the church of infinitesimals links to posts", in order to get support (like votes).

The one user170039 is referring to.

Simply Beautiful Art

That's.... weird

3:31 PM

Of course it is weird.

Simply Beautiful Art

:|

._.

@SimplyBeautifulArt You want to see plain evidence?

Simply Beautiful Art

Nah

The only reason I brought it in here was because I put the effort to type it up for him and he didn't respond to it

So yes constructive feedback in terms of did I do a shit awful job of explaining it

but now he has

@DavidReed A lot of users don't respond to answers. It can be annoying. Just too bad.

3:34 PM

I just felt bad because hes being taught that differentials actually MEAN something

Got to go.

See you all next time!

later

user131753

@DavidReed: This is the (very long) discussion of which I was talking about in this comment.

@LeakyNun Hey I put the sub(s,c,d) up for you

@LeakyNun if you scroll up you should be able to find it

user131753

@DavidReed: Also see this.

3:39 PM

Both you and him.

Its actually funny to watch

on the outside looking in

Why are you so driven to convince him?

I'm not trying to be abrasive. Just understand why everybody is on a mission to enlighten 21820

@LeakyNun Did you get the sub definition I gave you

user131753

@DavidReed I am not (and was not) trying to enlighten @user21820. I just wanted to know his philosophical position and wanted to get a feel for it.

Ah ok

I didn't sleep last night, so atm I have very little both in the way of a filter and in the way of a frontal lobe. My reaction to the links was just that people seem to push him very hard to agree with them

user131753

3:54 PM

In particular, I think that @user21820's philosophical position is very close to Realism and its always extremely enlightening to know the position of a realist in detail.

user131753

@DavidReed Then it would be better for you to take a good night's sleep and then look at those links.

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