On Monday, 29 August 2022 at 18:36:27 UTC+2, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
>
> > On Monday, 29 August 2022 at 16:19:01 UTC+2, Ben Bacarisse wrote:
> >> No I'm, not. Wij thinks I am because he does not know that there are
> >> two distinct definitions of limit
> > So you are outright admitting to equivocation! I thought so...
> I am struggling to accept that you are honestly this badly informed.
I am struggling to accept that you are trying to pin this on me! Mr "Usual Definitions".

You ARE equivocating. This is not my opinion. It's a fact! In accordance with the definition of "equivocation".

"In logic, equivocation ("calling two different things by the same name") is an informal fallacy resulting from the use of a particular word/expression in multiple senses within an argument."
> Surely this is just saying nonsense for the sake of saying anything to
> get off the hook?
Get fucked! I am not the one equivocating. If you don't care about clarity and avoiding logical fallacies (which actively harms understanding) just say so!

People who can't (self)reflect are the worst!

> > Given the TWO DISTINCT definitions of limit what's your
> > decision-procedure for selecting which definition to use.
> You just look at the lim. lim(x->oo) is the asymptotic limit and can't
> be defined in the same way as lim(x->c) where c is in R. Two utterly
> distinct situations need distinct definitions.
So why don't you have a notation for asymptotic and non-asymptotic limits?

That's so peculiar! The two functions even behave semantically differently!

> Please tell me you've know this all along? Why would you post anything
> on this topic if you did not know these basic facts?
Because the medium of communication (books!) is NOT conducive to encoding the polymorphic aspect of the lim() operator.

On the other hand source code IS conducive to encoding the polymorphic aspect of functions. I am sure you've heard of generics in programming language theory?

> Unfortunately I did not invent the notation and, in fact, it causes
> absolutely no confusion to any students I have every come across.
So the fact that every student of yours abandons the epsilon-delta method the moment they cross ocer into a Physics lecture was no signal of importance to you?

The fact that Physicists (to this day) use calculus with infinitesimals is of no importance to you?

> Except for you, but then I think you've know this all along, no? Were
> you really confused?
I am very confused. Just not about the topic you think I am confused about.

> Anyway, now you know what I mean when I say that 0.999... = 1. That
> took a long time.
No, I still don't. But hey! Keep lying to yourself.

>You "disagree" so presumably you have some other definition in mind.
Yes. I have told you my definition/theorem multiple times. (.999... = 1) ↔ False

>Maybe one day you will give it.
Maybe one day you'l acknowledge it.

> > Well, if pointing out THAT lim() is parametrically polymorphic is what
> > you mean by "pretending" then yes - I am "pretending".
> No, that's no what I meant. I meant pretending not to know in the plain
> sense of knowing all along what I meant by an infinite sum while asking
> me what I meant as if you didn't know -- ordinary pretending.
I didn't know what you meant by an infinite sum. That's why I asked.

In fact - you even admitted that your definitions (often) mean more than one thing! I know that. Which is precisely why I ask. So I can establish WHICH meaning you had in mind.

> Maybe you were not simply pretending not to know. Maybe you really did
> not know. But then why would you post on the topic?
To find out what you mean? Unequivocally.

> > I've been "pretending" all along that you are obscuring clarity by
> > using the SAME NAME for TWO DIFFERENT DEFINITIONS!
> You really just have to get used to that. Both are limits (so writing
> lim seems reasonable)
Both 1 and 2 are numbers, yet for some strange reason we use different symbols for them.
Both * and / are operators, yet for some strange reason we use different symbols for them.

>and I've never seen anyone else (well, excpt maybe
> Wij) get confused by the two forms since the symbol oo is obviously
> special since it's not in R.
It is obvious that ∞ is not in R. You've told us. But then you say stuff like "Element of R approaches ∞"

Indeed, I still struggle with the discontinuity from Finite -> Infinite values.

> >> The asymptotic limit is a function of real-valued functions. ∞ is not
> >> in the domain of the limit functor nor in the domain or co-domain of any
> >> function to which it can be applied.
> >
> > Ah! And what is your decision-procedure for
> > applicability/non-applicability?
> Ah! I see you cut the context because my answer points out that your
> question was daft.
Nonsense. My question is explicitly asking you for the source code of your dispatch procedure.

> As to your new question, see any good book on real analysis will explain
> how and when the lim operator can be applied.
That's very unfortunate - I can't explain English to a computer.

They are very.... particular... about equivocation.

> > Any "good" book on real analysis would NOT use the SAME NAME for TWO
> > DIFFERENT DEFINITIONS! Unless the theory was founded upon a foundation
> > which handles polymorphism.
> I think mathematics is not for you.
I think that's another fallacy. The No True Scottsman fallacy.

>All the texts will assume a level
> of sophistication and flexibility about notation that you find
> confusing.
ALL the texts? The source code of every proof assistant which implements Real analysis seems to be quite explicit about the polymorphism at play.

Maybe your encoding+medium is shit?

>Since it does not seem to cause problems for other students,
> I don't think anyone will write a text "good enough" for you.
Well, have you actually pointed out the logical issue to them? Or are you intentionally equivocating to avoid a student revolt?

> > And none of your foundations seem to hit that mark.
> Well, I am sorry about that. Is that why you up gave up on maths? It's
> use of notation is not sufficiently like programming abstractions?
That sounds like a perfectly good reason! Who doesn't want more+better abstractions?!?

Isn't that the entire point of Mathematics? Abstract reasoning!

> There is a great book called "The Mathematical Experience" that
> documents what mathematics really is by looking at what mathematicians
> actually do.
That sounds like a bit of a narrowly-focused text. They probably didn't look at what (meta)mathematicians (who are still mathematicians, by the way) actually do.

>In a case study it gives the Chinese remainder theorem in
> a whole bunch of formulations from ancient texts to modern books. The
> last example is a hyper-abstract (but hyper precise) definition from a
> CS text. The authors remark that "computer science in it's theoretical
> formulation is dominated by a spirit of abstraction which defers to no
> other branch of mathematics in its zealotry".
Ah. But that's just a matter of opinion!

Metamathematics is the Mathematics of Mathematics

> Most other mathematicians are quite relaxed about notation.
You call yourself "relaxed" ?!?!?! Hahahahahah!

You got super uptight about the "greater_than" and "nth_number_greater_than" notation!
And you are still avoiding the notational question about the "nth_successor_of_x"

> >> > You are binding "∞" to a parameter in Σ(n=0, ∞)!
> >> No, I'm not.
> > Really? So the usual Σ syntax can't be re-written in functional
> > notation as sigma(start, end, f) ?!?!
> Not in any useful way for real analysis, no. In the finite version,
> 'start' and 'end' will appear in the definition, but in the infinite
> case infinite case 'end' (to which oo would appear to be bound) will not
> appear.
That's utter nonsense. The behaviour of Σ literally changes depending on whether you put a 5 or a ∞ on its head!!!

> Topology (right up there in the abstraction stakes) is different, Wij
> was not taking about that, so neither am I.
Oh well. At least one of us is talking about topology and homotopy types.

> > Maybe you can give us the type-signature of Σ? That would help!
> Or you could learn about infinite sums before pontificating about them.
> (I know... neither of these will happen.)
Yeah, look - infinities are tricky things. You seem to have landed on the wrong side...

> I'll note that the vast majority of mathematicians would not care about
> the type signature of the summation operator. That's your CS
> abstraction zealotry coming out. "Sum" must be abstracted into one
> polymorphic functor!
That's absolute nonsense! The behaviour of Σ changes depending on whether you put a 5 or a ∞ on its head!
YOU have already abstracted it into one polymorphic functor!!!
The WAY you do algebra presently is polymorphic BY DEFAULT. You are manipulating reals together with integers together with rationals without a second thought!

And equality.... DAMN! Equality is basically one giant polymorphism because Univalence axiom!

> >> > What is the domain of Σ such that "∞" is in it?
> >> Likewise. The domain of Σ (in this case) is the set of functions from N
> >> to R.
> >
> > Wait a minute?!? Which parameter to Σ has the type N -> R ?!?!
> Whatever "parameter" (I wouldn't use that term) denotes the sequence
> being summed.
Uhm. That was the 3rd parameter to Σ(start, end, f)

What about the other two?
And what about the result?

I guess i really am wasting my time asking you for the meaning/type-signature of your function...

>But I don't insist on the severe all-encompassing
> abstractions that you appear to prefer -- this is just the infinite sum
> operator.
But it isn't an "infinite sum operator" if I put a finite number on top of Σ.

How difficult is this for you to grasp? Whether Σ is a "finite" or "infinite" sum operator depends DIRECTLY on the TYPE of parameter that goes on top of Σ

>Remember, for us relaxed mathematicians, there are two such
> operators, even though they look so very alike.
Let me remind you (again) how "relaxed" you got about the "nth_greater_than" operator....

> >> It seems that you think "∞" is problematic because you don't know how
> >> such limits are defined.
> >
> > That's an outright lie. ∞ is problematic because you are passing it as
> > a parameter to an iterator like Σ.
> No, no parameters. No passing. This is us hippy mathematicians happily
> using a notation that is not a parameterised, polymorphic abstraction.
> What's problematic is trying to shoehorn everything into your view of
> such abstractions.
You say "shoehorn" into polymorhism - I say "point out" polymorhism.

But it's difficult to recognize if you are terrible at (self)reflection.

> >>(The sums are also defined in terms of
> >> limits.)
> > But wait a minute! Aren't the limits defined in terms of sums?
> >
> > It sure seems to me you have a circular dependency?
> Only because you cut all the context. "The sums" are the sums in
> question, infinite sums, not all sums. They are defined in terms of
> limits of sums that are not the ones in question being simple finite
> sums. I don't think you are posting in good faith.
Says the guy who refuses to acknowledge his equivocation and blames me for it.

> > "I don't understand the difference between Nat -> Nat -> Bool and Nat
> > -> Nat -> Nat" (Ben Bacarisse, Aug 2022)
> Now I know you probably don't aspire to the highest moral standards, but
> you really should not pretend that that is a quote. You are free to
> think that that is what my words meant, but you should make it clear
> that it's your words and your opinion.
I am not at all pretending it's a quote. I am pretending THAT you meant what the text says.

Oh, and don't worry about the notation. Apparently, you Mathematicians, are relaxed about such stuff.