On Saturday, 3 September 2022 at 03:22:09 UTC+8, Keith Thompson wrote:
> wij <wyni...@gmail.com> writes:
> > On Friday, 2 September 2022 at 06:23:06 UTC+8, Keith Thompson wrote:
> >> wij <wyni...@gmail.com> writes:
> >> > On Thursday, 1 September 2022 at 03:05:16 UTC+8, Keith Thompson wrote:
> >> >> wij <wyni...@gmail.com> writes:
> >> >> > On Tuesday, 30 August 2022 at 23:30:28 UTC+8, Ben Bacarisse wrote:
> >> >> >> wij <wyni...@gmail.com> writes:
> >> >> >>
> >> >> >> > "1/3= 0.333... + nonzero_remainder" can be proved by contradiction.
> >> >> >> No it can't. With the usual meanings 1/3 = 0.333...
> >> >> >
> >> >> > Your only source of knowledge is the limit theory in the book (if dig deeper,
> >> >> > like most book-worm, lack concrete meaning, just words).
> >> >> > You keep evading the foundamental question and talk irrelevant superstition:
> >> >> > A logical deduction that lim(x->c) f(c)=L yields the conclusion f(c)=L (EQUAL).
> >> >> > Answer this question, everybody will be convinced.
> >> >> > Make sure you really solve it, because all such problems since at least
> >> >> > calculus was invented, will be solved by you !!!
> >> >> Answer what question?
> >> >>
> >> >> If that were a question, the answer would be no.
> >> >> You wrote:
> >> >> lim(x->c) f(c)=L yields the conclusion f(c)=L (EQUAL).
> >> >> I think you meant:
> >> >> lim(x->c) f(x)=L yields the conclusion f(c)=L (EQUAL).
> >> >> And I assume the added "(EQUAL)" was just for emphasis.
> >> >>
> >> >> No, lim(x->c) f(x)=L does not imply f(c)=L.
> >> >
> >> > Exactly what I mean.
> >> Oh? I still don't know what you were asking. You specifically
> >> challenged us to "Answer this question". Please tell us what
> >> question you were referring to.
> >
> > The conclusion from limit.
> "The conclusion from limit." is a sentence fragment, not a question.

If there is none, why you point me to the limit theory and indicate every should follow what?

> >> > This is my point: Limit cannot yield an equal conclusion .'lim' should
> >> > always stick to its expression, 'lim' cannot be removed. Otherwise, I ask for a
> >> > valid logic removing it from the limit expression to form an identity expression.
> >> > Or, I request a CONCLUSION suitable for all kind of further application,
> >> > e.g. lim(x->0) 1-x cannot yield 1-0=1 conclusion (by limit's δ-ϵ definition).
> >> > Same as lim 0.999...=1 cannot (logically) yield the conclusion 0.999...=1.
> >> lim(x->c) f(x)=L does not imply that f(c)=L.
> >> lim(x->c) f(x)=L does not imply that f(c)≠L.
> >> Sometimes it's equal, sometimes it isn't.
> >>
> >> The limit is equal to L. The value of f(c) may or may not be equal to L.
> >>
> >> I can't tell whether this addresses what you were talking about.
> >
> > Ok. So, explain why 0.999...=1, based on limit theory?
> > Nobody questions 0.9, 0.99,...,0.999... approaches 1. But how such limit
> > argument can lead to conclusion 0.999...=1?
> Is that the question you've been talking about? If so, that's
> disappointing, given your earlier claim:
> Answer this question, everybody will be convinced.
> Make sure you really solve it, because all such problems since at least
> calculus was invented, will be solved by you !!!
> Explaining why 0.999...=1 is not some intractable problem that has
> stymied mathematicians for centuries. It's nearly trivial.
>
> Do we even agree on what "0.999..." means? I say it means the limit of
> the sequence 0.9, 0.99, 0.999, 0.9999, etc. as the number of 9s
> increases without bound. The limit of that sequence is exactly 1.
> (No member of the sequence has the value 1.)
>
> Do you understand the previous paragraph? Do you agree? If not, please
> explain exactly what you disagree with.
>
> [...]
> >> If you don't understand how limits are conventionally defined, I suggest reading
> >> https://en.wikipedia.org/wiki/Limit_of_a_function#(%CE%B5,_%CE%B4)-definition_of_limit
> >> which explains it better than I probably could
> >
> > Why you people always like to convince yourself I don't understand limit?
> > It is you who don't understand what limit really is.
> OK, what is a limit? If you understand it and we don't, can you explain
> it to us?
>
> Have you read the definition I cited above? Do you think it's wrong?
> If so, what exactly is wrong with it?
> --
> Keith Thompson (The_Other_Keith) Keith.S.T...@gmail.com
> Working, but not speaking, for Philips
> void Void(void) { Void(); } /* The recursive call of the void */

Sorry, your reply read like a new comer to the "0.999...=1" problems.
You don't seem to understand the issues of limit.
You don't realize how broadly and how deeply "0.999...=1" problem involves.
I cannot possibly repeatedly explain these to you.

wij <wyniijj2@gmail.com> writes:

> On Friday, 2 September 2022 at 20:24:54 UTC+8, Ben Bacarisse wrote:
>> wij <wyni...@gmail.com> writes:
>>
>> > Ok. So, explain why 0.999...=1, based on limit theory?
>> So, just to be clear, you object to something you don't understand, yes?
>> You have not read an explanation of how the reals are defined?
>>
>> The set R is defined (note defined -- we choose this to be true) so that
>> every bounded monotonic sequence of rationals denotes a real number, a
>> number we call "the limit". Sometimes that might be another rational,
>> and sometimes we just accept that the limit is a number expressible only
>> by that and other limit expressions.
>
> Real numbers are not all constructable, not all are name-able.

Yes.

> Your theory of ℝ is flawed.

It's not mine. And since every theory is flawed, the theory of the
reals will have flaws as well. But even if it's flawed, you don't get
to say what everyone else means by 0.999....

> No need to fabricate any flawed ADVANCED MATH
> to 'prove'. As long as infinite long decimals are recognized as real number,
> kids can understand why. Not even high-school math is required to
> prove this claim.

I can't understand this. Is your object that the real numbers are not
simple enough. If you have a simpler definition of R, it would be very
well received. If you have defined another simpler set of numbers,
you'd have to say why anyone would be interested in it.

>> > Nobody questions 0.9, 0.99,...,0.999... approaches 1.
>> (I think there is a missing , there. If not, you have ended the
>> sequence with 1.)
>>
>> Yes. And it's a bounded monotonic sequence of rationals so by
>> definition it is one way to express some real number. What real number
>> could that be? The sequence surpasses every real that is less than 1
>> and yet is bounded above by one. 1 is the least upper bound of the
>> sequence. By definition, the sequence represents the real number 1.
>>
>> The definition of lim_{n->oo} S_n formalises this.
>
> Not interested in your flawed THEORY of real number.

Then don't waste my time by asking "So, explain why 0.999...=1, based on
limit theory?".

> Answer my specific questions.

As far as I know I have answered every question you've posed. The only
one I could find is "So, explain why 0.999...=1, based on limit theory?"
and you tell me you are not interested in the answer.

I think it would be simpler for me if I limited myself to correcting
any mistakes I spot.

>> > Why you people always like to convince yourself I don't understand
>> > limit?
>> Because you ask "explain why 0.999... = 1, based on limit theory". If
>> you asked why 2+2 = 4, I'd assume you don't understand arithmetic. If
>> you asked why the derivative of x^2 is 2x, I'd assume you don't
>> understand differential calculus.
>>
>> Even if you disagree with what you call "limit theory", you should
>> understand it before criticising it. You should be able to explain why
>> 0.999... = 1 yourself so that you objections could be taken seriously.
>> What's more, if you knew why 0.999... = 1 you'd be able to say exactly
>> what part of the explanation you object to and the discussion would
>> start from a position not yet reached.
>>
>
> My question is simple, clear and specific: A valid logic to remove 'lim' from
> a limit expression to form a conclusion. E.g. "lim 0.999...=1" (make it more
> formal the way you like) can yield the conclusion "0.999...=1".

There's no question here.

> Skep Dick already showed that you cannot even decide whether x-1 or x+1 is
> closer to infinity or not in expression "lim(x->∞) 1-1/10^x =
> 0.999...".

So what? I'm not going to explain (again) what those symbols mean
because you've just told me you are not interested in the theory of the
reals.

> Provide more specific explanations what you mean by the occurrence of
> infinity in text-books.

You are not interested in the theory of the reals, so why should I write
a book about for you?

> As said, there is no arithmetic rule applicable in limit
> calculation. If you are so confident. Please provide arithmetic/math
> rules in limit calculation that people can follow without ambiguity.

They are all available in standard books. But you've just said you are
not interested in the theory, so why do you care? Just keep telling
everyone they are wrong, and you'll get along just fine. Like PO, SD
and the others, you don't want to get a paper published, so just keep
posting here and be happy.

> Above are three KEY questions for you (if you insist the kid-understandable
> "0.999...∈ [0,1)" and "1/3= 0.333... + nonzero_remainer" are not correct).
> Better HONESTLY answer these three key questions.

Why? The every time I answer a question you either ignore the answer
(look above for an example of a multi-paragraph answer you simply
ignored) or tell me you are not interesting what I have to say.

> -----
> I say HONESTLY is because you like playing blind, ignoring facts with
> your smart talk you thought. You like to play smart, and had kept even
> playing smart before olcott. Even B.H. knew what you really did. The
> result was 'humiliated' by olcott. He is, in a way, smarter than you
> are. People can see. You just fool yourself by your own smart
> talk. 'crank', 'troll' is you. So, HONESTLY answer the questions. If
> you like to keep replying crap, save it.

I generally look to get information from people I think are
knowledgeable and smart. You don't think I am, so why keep asking me to
explain standard things you? You probably don't think Terrence Tao is
knowledgeable and smart because you rejected his book as well. If there
is no one you consider knowledgeable and smart, then there is no one who
can answer your questions in a way that you will pay attention to. You
are doomed to remain in ignorance of how real analysis is done.

--
Ben.

On 03/09/2022 06:31, wij wrote:
[to Ben:]
> Real numbers are not all constructable, not all are name-able.

True; and irrelevant. The theory of ℝ is different from that
of the computable numbers, and from that of the surreal numbers, and
from that of the complex numbers, and ....

> Your theory of ℝ is flawed.

"Different" is not the same as "flawed".

> No need to fabricate any flawed ADVANCED MATH
> to 'prove'. As long as infinite long decimals are recognized as real number,
> kids can understand why.

If it's all so simple, then you need to explain why it took over
2000 years to get from a recognition that some useful numbers are not
rational, to a workable knowledge of the different sorts of infinity and
to theories of computable numbers, etc.

[...]
> My question is simple, clear and specific: A valid logic to remove 'lim' from
> a limit expression to form a conclusion. E.g. "lim 0.999...=1" (make it more
> formal the way you like) can yield the conclusion "0.999...=1".

That's not a question, as others have pointed out. The best
sense I can make of your statement is that you want to know why the
limit of the sequence suggested by 0.9, 0.99, 0.999, ... being 1 means
that the limit of the sequence suggested by 0.9, 0.99, 0.999, ... is 1.
But that is trivial, and requires that you are using "0.999..." in two
different ways. But if you use "0.999..." consistently either to mean
the limit or the sequence, then you either are asking about "lim 1", or
are trying to equate a sequence to a number; neither of those seems to
be what you have in mind.

At the moment, you seem to be asking Ben and others to make
sense of some word salad that you produce. But even word salads need
context. What do /you/ mean by "0.999..."? A limit in ℝ? A sequence?
A rough equivalent to "0.(9)" with which we can follow rules with some
resemblance to Hackenbush [I call it "Hackenstrings"]? Something in
some number system other than ℝ, such as the hyperreals, surreals or
computables? What? At the moment, it's not possible even to guess.

> Skep Dick already showed that you cannot even decide whether x-1 or x+1 is
> closer to infinity or not in expression "lim(x->∞) 1-1/10^x = 0.999...".

Skep is a troll. If you ask meaningless questions, you will
get meaningless answers.

> Provide more specific explanations what you mean by the occurrence of infinity
> in text-books.
> As said, there is no arithmetic rule applicable in limit calculation. If you are so
> confident. Please provide arithmetic/math rules in limit calculation that people
> can follow without ambiguity.

As others have said, if you can explain what problems you are
having with specific wording in textbooks, then we can help. But they
are likely to be talking about ℝ; if you want to know about other sorts
of number, then you need to specify which. It would also help if you
didn't falsely accuse Ben [in particular] of dishonesty; unlike some
in this NG, he tries very hard to be helpful.

--
Andy Walker, Nottingham.
Andy's music pages: www.cuboid.me.uk/andy/Music
Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Herold

On Saturday, 3 September 2022 at 20:32:19 UTC+8, Ben Bacarisse wrote:
> wij <wyni...@gmail.com> writes:
>
> > On Friday, 2 September 2022 at 20:24:54 UTC+8, Ben Bacarisse wrote:
> >> wij <wyni...@gmail.com> writes:
> >>
> >> > Ok. So, explain why 0.999...=1, based on limit theory?
> >> So, just to be clear, you object to something you don't understand, yes?
> >> You have not read an explanation of how the reals are defined?
> >>
> >> The set R is defined (note defined -- we choose this to be true) so that
> >> every bounded monotonic sequence of rationals denotes a real number, a
> >> number we call "the limit". Sometimes that might be another rational,
> >> and sometimes we just accept that the limit is a number expressible only
> >> by that and other limit expressions.
> >
> > Real numbers are not all constructable, not all are name-able.
> Yes.
> > Your theory of ℝ is flawed.
> It's not mine. And since every theory is flawed, the theory of the
> reals will have flaws as well. But even if it's flawed, you don't get
> to say what everyone else means by 0.999....
> > No need to fabricate any flawed ADVANCED MATH
> > to 'prove'. As long as infinite long decimals are recognized as real number,
> > kids can understand why. Not even high-school math is required to
> > prove this claim.
> I can't understand this. Is your object that the real numbers are not
> simple enough. If you have a simpler definition of R, it would be very
> well received. If you have defined another simpler set of numbers,
> you'd have to say why anyone would be interested in it.
> >> > Nobody questions 0.9, 0.99,...,0.999... approaches 1.
> >> (I think there is a missing , there. If not, you have ended the
> >> sequence with 1.)
> >>
> >> Yes. And it's a bounded monotonic sequence of rationals so by
> >> definition it is one way to express some real number. What real number
> >> could that be? The sequence surpasses every real that is less than 1
> >> and yet is bounded above by one. 1 is the least upper bound of the
> >> sequence. By definition, the sequence represents the real number 1.
> >>
> >> The definition of lim_{n->oo} S_n formalises this.
> >
> > Not interested in your flawed THEORY of real number.
> Then don't waste my time by asking "So, explain why 0.999...=1, based on
> limit theory?".
>
> > Answer my specific questions.
>
> As far as I know I have answered every question you've posed. The only
> one I could find is "So, explain why 0.999...=1, based on limit theory?"
> and you tell me you are not interested in the answer.
>
> I think it would be simpler for me if I limited myself to correcting
> any mistakes I spot.
> >> > Why you people always like to convince yourself I don't understand
> >> > limit?
> >> Because you ask "explain why 0.999... = 1, based on limit theory". If
> >> you asked why 2+2 = 4, I'd assume you don't understand arithmetic. If
> >> you asked why the derivative of x^2 is 2x, I'd assume you don't
> >> understand differential calculus.
> >>
> >> Even if you disagree with what you call "limit theory", you should
> >> understand it before criticising it. You should be able to explain why
> >> 0.999... = 1 yourself so that you objections could be taken seriously.
> >> What's more, if you knew why 0.999... = 1 you'd be able to say exactly
> >> what part of the explanation you object to and the discussion would
> >> start from a position not yet reached.
> >>
> >
> > My question is simple, clear and specific: A valid logic to remove 'lim' from
> > a limit expression to form a conclusion. E.g. "lim 0.999...=1" (make it more
> > formal the way you like) can yield the conclusion "0.999...=1".
> There's no question here.
> > Skep Dick already showed that you cannot even decide whether x-1 or x+1 is
> > closer to infinity or not in expression "lim(x->∞) 1-1/10^x =
> > 0.999...".
> So what? I'm not going to explain (again) what those symbols mean
> because you've just told me you are not interested in the theory of the
> reals.
> > Provide more specific explanations what you mean by the occurrence of
> > infinity in text-books.
> You are not interested in the theory of the reals, so why should I write
> a book about for you?
> > As said, there is no arithmetic rule applicable in limit
> > calculation. If you are so confident. Please provide arithmetic/math
> > rules in limit calculation that people can follow without ambiguity.
> They are all available in standard books. But you've just said you are
> not interested in the theory, so why do you care? Just keep telling
> everyone they are wrong, and you'll get along just fine. Like PO, SD
> and the others, you don't want to get a paper published, so just keep
> posting here and be happy.
> > Above are three KEY questions for you (if you insist the kid-understandable
> > "0.999...∈ [0,1)" and "1/3= 0.333... + nonzero_remainer" are not correct).
> > Better HONESTLY answer these three key questions.
> Why? The every time I answer a question you either ignore the answer
> (look above for an example of a multi-paragraph answer you simply
> ignored) or tell me you are not interesting what I have to say.
> > -----
> > I say HONESTLY is because you like playing blind, ignoring facts with
> > your smart talk you thought. You like to play smart, and had kept even
> > playing smart before olcott. Even B.H. knew what you really did. The
> > result was 'humiliated' by olcott. He is, in a way, smarter than you
> > are. People can see. You just fool yourself by your own smart
> > talk. 'crank', 'troll' is you. So, HONESTLY answer the questions. If
> > you like to keep replying crap, save it.
> I generally look to get information from people I think are
> knowledgeable and smart. You don't think I am, so why keep asking me to
> explain standard things you? You probably don't think Terrence Tao is
> knowledgeable and smart because you rejected his book as well. If there
> is no one you consider knowledgeable and smart, then there is no one who
> can answer your questions in a way that you will pay attention to. You
> are doomed to remain in ignorance of how real analysis is done.
>
> --
> Ben.

I could not possibly expect your standard things, I was originally seeking for
opinion and help about MY OWN IDEA. What I did is following the trend.

I don't complain Tao (and others), who was likely in 'the system' all his life
devoting what he could.

On Saturday, 3 September 2022 at 22:07:58 UTC+8, Andy Walker wrote:
> On 03/09/2022 06:31, wij wrote:
> [to Ben:]
> > Real numbers are not all constructable, not all are name-able.
> True; and irrelevant. The theory of ℝ is different from that
> of the computable numbers, and from that of the surreal numbers, and
> from that of the complex numbers, and ....
> > Your theory of ℝ is flawed.
> "Different" is not the same as "flawed".
> > No need to fabricate any flawed ADVANCED MATH
> > to 'prove'. As long as infinite long decimals are recognized as real number,
> > kids can understand why.
> If it's all so simple, then you need to explain why it took over
> 2000 years to get from a recognition that some useful numbers are not
> rational, to a workable knowledge of the different sorts of infinity and
> to theories of computable numbers, etc.
>
> [...]
> > My question is simple, clear and specific: A valid logic to remove 'lim' from
> > a limit expression to form a conclusion. E.g. "lim 0.999...=1" (make it more
> > formal the way you like) can yield the conclusion "0.999...=1".
> That's not a question, as others have pointed out. The best
> sense I can make of your statement is that you want to know why the
> limit of the sequence suggested by 0.9, 0.99, 0.999, ... being 1 means
> that the limit of the sequence suggested by 0.9, 0.99, 0.999, ... is 1.
> But that is trivial, and requires that you are using "0.999..." in two
> different ways. But if you use "0.999..." consistently either to mean
> the limit or the sequence, then you either are asking about "lim 1", or
> are trying to equate a sequence to a number; neither of those seems to
> be what you have in mind.
>
> At the moment, you seem to be asking Ben and others to make
> sense of some word salad that you produce. But even word salads need
> context. What do /you/ mean by "0.999..."? A limit in ℝ? A sequence?
> A rough equivalent to "0.(9)" with which we can follow rules with some
> resemblance to Hackenbush [I call it "Hackenstrings"]? Something in
> some number system other than ℝ, such as the hyperreals, surreals or
> computables? What? At the moment, it's not possible even to guess.
> > Skep Dick already showed that you cannot even decide whether x-1 or x+1 is
> > closer to infinity or not in expression "lim(x->∞) 1-1/10^x = 0.999...".
> Skep is a troll. If you ask meaningless questions, you will
> get meaningless answers.
> > Provide more specific explanations what you mean by the occurrence of infinity
> > in text-books.
> > As said, there is no arithmetic rule applicable in limit calculation. If you are so
> > confident. Please provide arithmetic/math rules in limit calculation that people
> > can follow without ambiguity.
> As others have said, if you can explain what problems you are
> having with specific wording in textbooks, then we can help. But they
> are likely to be talking about ℝ; if you want to know about other sorts
> of number, then you need to specify which. It would also help if you
> didn't falsely accuse Ben [in particular] of dishonesty; unlike some
> in this NG, he tries very hard to be helpful.
>
> --
> Andy Walker, Nottingham.
> Andy's music pages: www.cuboid.me.uk/andy/Music
> Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Herold

Lots of my response to the above would be duplicated, so I took the liberty to
save it. My purpose is not arguing with your belief.
You have made your stance clear. Mine should also be clear by now.

Andy Walker <anw@cuboid.co.uk> writes:

> At the moment, you seem to be asking Ben and others to make
> sense of some word salad that you produce. But even word salads need
> context. What do /you/ mean by "0.999..."? A limit in ℝ? A sequence?
> A rough equivalent to "0.(9)" with which we can follow rules with some
> resemblance to Hackenbush [I call it "Hackenstrings"]? Something in
> some number system other than ℝ, such as the hyperreals, surreals or
> computables? What? At the moment, it's not possible even to guess.

Well, I have a few guesses... My first guess is that it won't be
anything anyone else has come up with. My second guess is that it's not
a new set of numbers but a critique of everything conventional centred
around 0.999... = 1 denial.

And there's really only one kind of 0.999... = 1 denier these days.
Nowadays pretty much every 'alternative thinker' who posts about maths
is, in fact, a programmer, so 0.999... is a process, maybe even an
actual algorithm. Since it never gets to 1 (in this case), the equality
is obviously wrong as any fule kno. It's so clear to them that they
can't be bothered to find out what anyone else really means.

Limits (some, most, all?) must be left as limits and never resolved to
be equal to anything because the code doesn't get there.

The central lacuna is not seeing that the equality means it's the
process that is equal to 1, not that 1 is reached. The reals /are/ the
Dedkind cuts, or they /are/ the equivalence classes of Cauchy sequence.

All just guesses of course...

PS. Thanks for your kind remarks.

--
Ben.

On 9/3/2022 9:07 AM, Andy Walker wrote:
> On 03/09/2022 06:31, wij wrote:
> [to Ben:]
>> Real numbers are not all constructable, not all are name-able.
>
>     True;  and irrelevant.  The theory of ℝ is different from that
> of the computable numbers, and from that of the surreal numbers, and
> from that of the complex numbers, and ....
>
>> Your theory of ℝ is flawed.
>
>     "Different" is not the same as "flawed".
>
>>                   No need to fabricate any flawed ADVANCED MATH
>> to 'prove'. As long as infinite long decimals are recognized as real
>> number,
>> kids can understand why.
>
>     If it's all so simple, then you need to explain why it took over
> 2000 years to get from a recognition that some useful numbers are not
> rational, to a workable knowledge of the different sorts of infinity and
> to theories of computable numbers, etc.
>
> [...]
>>   My question is simple, clear and specific: A valid logic to remove
>> 'lim' from
>>   a limit expression to form a conclusion. E.g. "lim 0.999...=1" (make
>> it more
>>   formal the way you like) can yield the conclusion "0.999...=1".
>
>     That's not a question, as others have pointed out.  The best
> sense I can make of your statement is that you want to know why the
> limit of the sequence suggested by 0.9, 0.99, 0.999, ... being 1 means
> that the limit of the sequence suggested by 0.9, 0.99, 0.999, ... is 1.
> But that is trivial, and requires that you are using "0.999..." in two
> different ways.  But if you use "0.999..." consistently either to mean
> the limit or the sequence, then you either are asking about "lim 1", or
> are trying to equate a sequence to a number;  neither of those seems to
> be what you have in mind.
>
>     At the moment, you seem to be asking Ben and others to make
> sense of some word salad that you produce.  But even word salads need
> context.  What do /you/ mean by "0.999..."?

Dead frogs eating boulders for lunch?

> A limit in ℝ?  A sequence?
> A rough equivalent to "0.(9)" with which we can follow rules with some
> resemblance to Hackenbush [I call it "Hackenstrings"]?  Something in
> some number system other than ℝ, such as the hyperreals, surreals or
> computables?  What?  At the moment, it's not possible even to guess.
>
>>   Skep Dick already showed that you cannot even decide whether x-1 or
>> x+1 is
>>   closer to infinity or not in expression "lim(x->∞) 1-1/10^x =
>> 0.999...".
>
>     Skep is a troll.  If you ask meaningless questions, you will
> get meaningless answers.
>
>>   Provide more specific explanations what you mean by the occurrence
>> of infinity
>>   in text-books.
>>   As said, there is no arithmetic rule applicable in limit
>> calculation. If you are so
>> confident. Please provide arithmetic/math rules in limit calculation
>> that people
>> can follow without ambiguity.
>
>     As others have said, if you can explain what problems you are
> having with specific wording in textbooks, then we can help.  But they
> are likely to be talking about ℝ;  if you want to know about other sorts
> of number, then you need to specify which.  It would also help if you
> didn't falsely accuse Ben [in particular] of dishonesty;  unlike some
> in this NG, he tries very hard to be helpful.
>

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

wij <wyniijj2@gmail.com> writes:
> On Saturday, 3 September 2022 at 03:22:09 UTC+8, Keith Thompson wrote:
>> wij <wyni...@gmail.com> writes:
>> > On Friday, 2 September 2022 at 06:23:06 UTC+8, Keith Thompson wrote:
>> >> wij <wyni...@gmail.com> writes:
>> >> > On Thursday, 1 September 2022 at 03:05:16 UTC+8, Keith Thompson wrote:
>> >> >> wij <wyni...@gmail.com> writes:
>> >> >> > On Tuesday, 30 August 2022 at 23:30:28 UTC+8, Ben Bacarisse wrote:
>> >> >> >> wij <wyni...@gmail.com> writes:
>> >> >> >>
>> >> >> >> > "1/3= 0.333... + nonzero_remainder" can be proved by contradiction.
>> >> >> >> No it can't. With the usual meanings 1/3 = 0.333...
>> >> >> >
>> >> >> > Your only source of knowledge is the limit theory in the book (if dig deeper,
>> >> >> > like most book-worm, lack concrete meaning, just words).
>> >> >> > You keep evading the foundamental question and talk irrelevant superstition:
>> >> >> > A logical deduction that lim(x->c) f(c)=L yields the conclusion f(c)=L (EQUAL).
>> >> >> > Answer this question, everybody will be convinced.
>> >> >> > Make sure you really solve it, because all such problems since at least
>> >> >> > calculus was invented, will be solved by you !!!
>> >> >> Answer what question?
>> >> >>
>> >> >> If that were a question, the answer would be no.
>> >> >> You wrote:
>> >> >> lim(x->c) f(c)=L yields the conclusion f(c)=L (EQUAL).
>> >> >> I think you meant:
>> >> >> lim(x->c) f(x)=L yields the conclusion f(c)=L (EQUAL).
>> >> >> And I assume the added "(EQUAL)" was just for emphasis.
>> >> >>
>> >> >> No, lim(x->c) f(x)=L does not imply f(c)=L.
>> >> >
>> >> > Exactly what I mean.
>> >> Oh? I still don't know what you were asking. You specifically
>> >> challenged us to "Answer this question". Please tell us what
>> >> question you were referring to.
>> >
>> > The conclusion from limit.
>> "The conclusion from limit." is a sentence fragment, not a question.
>
> If there is none, why you point me to the limit theory and indicate
> every should follow what?

OK, let's step back a bit and keep it simple.

You challenged us to "Answer this question".

I don't know what question you're referring to.

Please reply to this with the actual question, phrased as a question.

[...]

--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Philips
void Void(void) { Void(); } /* The recursive call of the void */

On 9/3/2022 3:43 PM, olcott wrote:
<snip>
> Dead frogs eating boulders for lunch?
<snip>

That's the first intelligent thing you've said in any message in any of
the dozens of POOP threads that still survive. Maybe there's hope for
you yet! Did you make it up or spot it someplace else? It's so hard to
tell because you so often copy technical wisdom out of context that
doesn't apply where you paste it. But this time you knocked it out of
the park! Congratulations from all of us.

I see that you had the foresight to copyright it, so let's hope that
it's actually yours.
--
Jeff Barnett