Skep Dick <skepdick22@gmail.com> writes:

> 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".

Whose fault is it that you won't look up how limits are defined? Not
mine.

> 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."

The expressions are clearly distinct. There is no equivocating.

>> > 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?

It's right there. For some reason you claim you can't see the
difference.

>> 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.

Ah, I thought you might have trouble with book learning. Unfortunately
authors are not going to accommodate your desire to have material
presented in one pointlessly uniform way.

> 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?

If they did (and I have no idea if they did) why would I care?

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

I'm interested in infinitesimals. I like infinitesimals. I wish the
0.999... = 1 deniers knew how to use them.

>> 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.

Well I think you are stuck then. Do you always join in discussions even
when you don't know what's being talked about?

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

You think that's a definition? Well at least we can be sure you won't
be writing any books about the topic!

But please, don't feel you have to say anything more. If you've said as
much as you can, let's leave it at that.

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

Aw, now that's disappointing. It's right there on the Usenet crank
bingo card.

>> ... 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.

OK. And now we know that you don't like maths books, so we are at an
impasse. Try to keep your objections to what I wrote in proportion to
the degree to with you don't know what I mean.

> In fact - you even admitted that your definitions (often) mean more
> than one thing!

No. The definitions mean only one thing.

>> 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 ∞"

Gosh, where? Let me correct that right away. I can't find the post
where I said that so can you give me the message ID? (Please don't let
this be another dishonest non quote.)

>> >> 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.

No, the question I replied to with the text above was "What is the
domain of lim such that "∞" is in it?". You presumably know (now) what a daft
question that was so you are pretending you were asking for a
"decision-procedure" all along. You weren't. You asked a silly question.

>> > 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.

Yes, it would be if I were making a logical argument. But I am just
making the observation that you don't appear to be a true Scotsman --
that mathematics is not for you. You can agree or disagree since it's
opinion and not a logical deduction.

>> 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.

I am happy if you have found the rigorous "polymorphic" lim operator you
wanted. Do you still not know what I mean by 0.999... = 1? If not,
then what good was this suitably abstract text?

>> 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!

Uptight? No, quite relaxed about that too.

> And you are still avoiding the notational question about the
> "nth_successor_of_x"

Yes, still just loving the fact that you can answer "What's the 0th
integer greater than 4?" with "It's 4!". Classic!

>
>> >> > 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!!!

Hmm... That's what I said only I gave more detail. Oh well, I think
there will be little understanding between us on any topic now.

>> 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!

You know all this about what I'm doing but you don't know what I mean by
0.999... = 1. Yeah, right!

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

Yes, you are. I not going to write a textbook on real analysis for you
no matter how often you ask.

>> 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.

Yes, because that, in my view, is a different operator, despite the
apparent similarity. You can force any two functions into one if like.
You can have a sin_cos function that is either depending on the
arguments, but infinite sums are not defined in the same way as finite
sums so I have no interest in your shoehorning exercise. It's
abstraction for its own sake.

> 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

I fully understand that you'd like it to be defined that way. Go ahead
and write it up if you want. I don't want two kinds of sum to be
unified like that.

>> > "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.

Don't try to wriggle out of it. Own it. You deliberately echoed my
quotation of your words so as to make readers think these were my words.
That's not an honest way to engage in a discussion.

--
Ben.
"What's the 0th integer greater than 4? It's 4!" (Skep Dick, Aug 2022)
(That /is/ a quotation. Message-ID:
<0ac9a8fa-a86e-4f2a-b60b-cb78659fe0d9n@googlegroups.com>)