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>>> the day he first saw the magic mountain. He got on the computer to order
>>> something zesty from HelloFresh. After choosing the closest to a healthy
>>> nice pre-agricultural food kit, he clicked, "Go to checkout" button,
>>> after which the computer waited for a few seconds but instead of getting
>>> to the check out screen, a screen came up to make sure Physfit was not a
>>> robot. It had a simple question that he had to give it the correct
>>> answer, otherwise food nommo.
>>>
>>> The question went like this:
>>>
>>>      "In math, is there a difference between the two numbers
0.999999...
>>> and 1 ?"
>>>
>>> The digits of "9" continued forever to the right of the radix point. So
>>> of course, Physfit clicked on the "yes" button. If there was not a
>>> difference, then one wouldn't even bother to write 1 in that funky form,
>>> using an infinite series of digit 9.
>>>
>>> But the screen disappeared, and a message said, "You're a robot. Bye!"
>>>
>>> Physfit said, "Fuck!" (first of the fix number of curses Jesus had
>>> allowed him for that day). So he took a pen and paper and started
>>> jotting down:
>>>
>>>      x = 0.99999....
>>>
>>> Therefore:
>>>
>>>      10x = 9.99999....
>>>
>>> Now he subtracted the former from the latter:
>>>
>>>      10x - x = 9.99999... - 0.99999...
>>>
>>> Which simplifies to:
>>>
>>>      9x = 9
>>>
>>> And therefore:
>>>
>>>      x = 1
>>>
>>> "What the fuck??", said Physfit (his 2nd curse of the day).
>>>
>>> Why x which was 0.99999... and not 1, turned out to be 1? ... "
>>>
>>>
>>> (end of quote)
>>>
>>>
>>> So, is this problem pointing to what Kosmanson has been so keen
>>> about? :)
>>>
>>>
>>>
>>>
>>>
>>
>> Once I was reading a book or article,
>> and was introduced the introduction of .999 (...),
>> vis-a-vis, 1. A cohort of subjects was surveyed
>> their opinion and belief whether .999, dot dot dot,
>> was equal to, or less than, one. About half said
>> same and about half said different.
>>
>>
>> It's two different natural notations that happen
>> to collide and thus result being ambiguous.
>>
>> So, then these days we have the laws of arithmetic
>> introduced in primary school, usually kindergarten,
>> about the operations on numbers, and also inequalities,
>> and the order in numbers.
>>
>> Yet, even the usual account of addition and its
>> inverse and its recursion and that's inverse,
>> as operators, of whole numbers, has a different
>> account, of increment on the one side, and, division
>> on the other, sort of like the Egyptians only had
>> division or fractions and Egyptian fractions,
>> and tally marks are only increment, that though
>> it was the Egyptian fractions that gave them a
>> mathematics, beyond the simplest sort of conflation
>> of "numbering" and "counting".
>>
>> So, where ".999 vis-a-vis 1" has a deconstructive account,
>> to eliminate its ambiguities with respect to what it's
>> to model, or the clock-arithmetic and field-arithmetic,
>> even arithmetic has a deconstructive account, then,
>> even numbering versus counting has a deconstructive account,
>> to help eliminate what are the usually ignored ambiguities.
>>
>>
>> So, pre-calculus, the course, goes to eliminate or talk
>> away the case .999, dot dot dot, different 1. Yet,
>> it can be reconstrued and reconstructed, on its own
>> constructive account. So, it's a convention.
>>
>>
>> It's "multiplicity theory", see, that any, "singularity
>> theory", which results as of admitting only the principal
>> branch of otherwise a "bifurcation" or "opening" or "catastrophe"
>> or "perestroika (opening)", as they are called in mathematics,
>> branches, that singularity theory is a multiplicity theory,
>> yet the usual account has that it's just nothing,
>> or that it's apeiron and asymptotic.
>>
>>
>> So, there's a clock arithmetic where there's a reason why
>> that there's a .999, dot dot dot, _before_ 1.0, in the
>> course of passage of values from 0, to 1, and, it's also
>> rather particularly only between 0 and 1, as what results
>> thusly a whole, with regards to relating it to the modularity
>> of integers, the integral moduli.
>>
>> Thusly, real infinity has itself correctly and constructively
>> back in numbers for "standard infinitesimals" here called
>> "iota-values".
>>
>> Then, this is totally simple and looks like f(n) = n/d,
>> for n goes from zero to d and d goes to infinity, this
>> is a limit of functions for this function which is not-
>> a- real- function yet is a nonstandard function and that
>> has real analytical character, it's a discrete function
>> that's integrable and whose integral equals 1, it illustrates
>> a doubling-space according to measure theory in the measure problem,
>> it's its own anti-derivative so all the tricks about the exponential
>> function in functional analysis have their usual methods about it,
>> it's also a pdf and CDF of the natural integers at uniform random,
>> of which there are others, because there are at least three laws
>> of large numbers, at least three Cantor spaces, at least three
>> models of continuous domains, and, at least three probability
>> distributions of the naturals at uniform random.
>>
>> So, "iota-values" are not the same thing as the raw differential,
>> which differential analysts will be very familiar with as usually
>> not- the- raw- differential yet only as under the integral bar
>> in the formalism, yet representing about the solidus or divisor bar
>> the relation of two quantities algebraically, then indeed there's
>> that "iota-values" are as of some "standard infinitesimals", yet
>> only under the limit of function the "natural/unit equivalency function"
>> the N/U EF, about [0,1]. This thus results a model of
>> a continuous domain "line reals" to go along with the usual standard
>> linear curriculum's "field reals" then furthermore later there's
>> a "signal reals" of at least these three models of continuous domains.
>>
>>
>> The usual demonstration after introducing the repeating terminus
>> and using algebra to demonstrate a fact about arithmetic,
>> is good for itself, and is one of the primary simplifications
>> of the linear curriculum, yet as a notation, it's natural that
>> two different systems of notation can see it variously, then
>> that it merely demands a sort of book-keeping, to disambiguate it.
>>
>> If you ever wonder why mathematics didn't have one of these,
>> or, two of these as it were together, it does, and it's only
>> a particular field of mathematics sort of absent the super-classical
>> and infinitary reasoning, that doesn't.
>>
>> Then at least we got particle/wave duality as super-classical,
>> then Zeno's classical expositions of the super-classical were
>> just given as that the infinite limit as introduced in pre-calculus
>> said we could ignore the deductive result that it really must complete,
>> the geometric series.
>
> Then again, one can define the reals as the convergences of uncountably
> infinitely many infinite series. There is no differece between 0.999...
> and 1, they are simply two different representations of the same
> mathematical object.


Bullshit. The point in question is exactly whether what you say is
bullshit :)

The answer to the baby problem shows, quite simply, that X is indeed
0.9999... and _certainly_ not 1.

Physics, only in its most useful form for humans, can speak for

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