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Topic: RE: Matheology 400: Quantifier Confusion
Replies: 188   Last Post: Dec 13, 2013 5:48 AM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology 400: Quantifier Confusion
Posted: Dec 7, 2013 9:30 PM

WM <wolfgang.mueckenheim@hs-augsburg.de> wrote:
> Am Samstag, 7. Dezember 2013 01:28:48 UTC+1 schrieb Zeit Geist:
> > 2) It is impossible to distinguish a real number d by its digits from all
> > other real numbers. (Proof by the fact that every FIS(d_n) = d_1, ..., d_n
> > is shared by uncountably many real numbers.)

> > > It is. Simple exercise: Try to to distinguish 0.111... by writing
> > > arbitraily many 1's from all its FIS.

> > I don't write 1/9 as an arbitrary number of 1's (well maybe Informally ),
> > but as the formula

> Then it belongs to the set of finite definitions - like every irrational
> number you can define.

> > 1/9 = { a_i | A( i e N )( a_i = 1 ) }.
> > This is distinguishable by from All FIS of 1/9, as for any, all and every
> > FIS there is a decimal place that is a 0.

> Of course, but it is not an infinite string of digits but only defines an
> infinite string of digits.

And WM has never given us anything but the names of numbers, never a
number itself, so is in no position to quibble.

> > > Further: If we know that for every n in |N: d_n = 1, then we know that
> > > every decimal is 1m then d = 1/9 in decimals.
> > > If we know that for every n in |N, d_n is in a rational number, then d
> > > csannot be an irrational number.

> > What?
> > So, you found an example of a sequence of rationals that has a rational
> > limit.

> I found that every limit can only be given as a finite definition.

But WM has just argued that every limit of a sequence of rational
numbers must be a rational number, which is nonsense.

Each of s_n = sum_(k = 0..n) 1/k! is rational,
but s_oo = e , which is not.

> > Hence you conclude, All sequences of rationals Must have a rational limit.

> No, I conclude that every string of digits that has only digits at indexed
> places is a rational number.

So sum_(k = 0..oo) 1/10^n! is rational?

> > Such a Mastery of Logic, Dear Professor!
> You see, as usual you have only failed to understand.

Failing to understand nonsense is no bad thing.

> > You may claim that "Actual Infinity" does Not Exist, and reject the AoI.
> I do not reject AoT

But you do reject the AoI, which was the point at issue.

> but the interpretation of set that is unjustufied because
> "set" has no definition.

"Set" has all sorts of definitions, but for WM to accept any of them
would pin him down to dull reality rather than drifting around in the
dreamworld of his WMytheology
> > But, you do more than that. You claim that its acceptance must and will

WM's claims to show things never survive outside of WM's wild weird
world of WMytheology.

> > Every Mathematicians of Modern Times that you cite on your list of people
> > who reject "Actual Infinity", reject it one Philosophical Grounds.

> No. There are some who have recognized that the switching between actual and
> potential is the reason.

Some of us merely reject your "potentia"l as undefineable nonsense.

> If I was the first to recognize the inconsistency it would nevertheless be an
> inconsistency.

As ther are far more inconsisteneis inside WM's WMytheology that
outside of it, those striving consistency should avoid WMytheology like
plague.
> I showed how you try to veil it:
> You say for every rational in a rationals complete list, we can find a digit
> where it differs from the d.
> That is enough to show that d differs from all rationals.

> Quantifier confusion which leads to a mistake since every d that is only
> defined by its digits is a rational number and, therefore, cannot differ from
> all rational numbers.

More of Wm's nonsense! There aer all sorts of numbers defined by digits
which are not rational, like a number with 0 in every composite decimal
place and 1 in every prime decimal place.

> You nevertheless insist that d differs from the list. None of its FIS
> differs. But you refuse to say what the difference between d and all its FIS
> is.

The difference between d and its FISs is the finiteness or infiniteness
of the number of decimal places required. A FIS of d, a d_n, only
requires finitely many, but d itself requires more thatn any finite
number of them.
> You are a Crank!

Actually there is far better evidence for the crankhood of WM than for
that of any of his critics.

> > > > But, I don't expect you to understand why.
> > > Explain the reason. Explain how d can stretch beyond every d_n. If it
> > > does not, it is a FIS.

> > Because d is Not a FIS, duh!

> What is the difference (in terms of digits which only can differ from digits)
> between d and all its FIS?

The difference between d and its FISs is the finiteness or infiniteness
of the number of decimal places required. A FIS of d, a d_n, only
requires finitely many, but d itself requires more thatn any finite
number of them.
Anyone not aware of that difference is just not paging attention.

So wake up, WM, and start paying attention!

> > For all n, d contains a non-zero digit where d_n contains a zero.
> > That is, if d is irrational or a non-repeating non-terminating rational.

> You wanted to say "for every n" but tha is not enough because we have seen
> above that if d is irrational it cannot be listed didgit by digit.

Many of them can be so listed everywhere but in WM's wild weird world
of WMytheology.

> It is impossible to leave that circle: Every digit d_n that could differ
> from a rational number is itself belonging to a rational number.

Digits are not only all rational but are all integral and all natural.

> You try to sell the trick that a rational number can differ from all
> rationals numbers.

It certainly can differ from al OTHER rational numbers, but there is no
compulsion for an anti-diagonal to be reational, and a high probability
that it won't be.

> Can you understand at least that every digit of an irrational number (that
> can be written or calculated by a finite formula) belongs to a rational
> approximation of this number?

It also belongs to a really finite set of digits, ten for a decimal
relresentataion.

> It is impossible that any rational
> approximation differs from all rational approximations.

It can easily differ from all but one.
--

Date Subject Author
12/4/13 Tucsondrew@me.com
12/4/13 wolfgang.mueckenheim@hs-augsburg.de
12/4/13 fom
12/4/13 wolfgang.mueckenheim@hs-augsburg.de
12/4/13 fom
12/4/13 Tucsondrew@me.com
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Tucsondrew@me.com
12/5/13 Virgil
12/5/13 Tucsondrew@me.com
12/6/13 wolfgang.mueckenheim@hs-augsburg.de
12/6/13 Tucsondrew@me.com
12/6/13 wolfgang.mueckenheim@hs-augsburg.de
12/6/13 Virgil
12/6/13 Tucsondrew@me.com
12/7/13 wolfgang.mueckenheim@hs-augsburg.de
12/7/13 Virgil
12/8/13 wolfgang.mueckenheim@hs-augsburg.de
12/8/13 Virgil
12/6/13 wolfgang.mueckenheim@hs-augsburg.de
12/6/13 Virgil
12/7/13 wolfgang.mueckenheim@hs-augsburg.de
12/7/13 Virgil
12/6/13 Tucsondrew@me.com
12/7/13 wolfgang.mueckenheim@hs-augsburg.de
12/7/13 Virgil
12/7/13 Virgil
12/8/13 wolfgang.mueckenheim@hs-augsburg.de
12/8/13 Virgil
12/6/13 fom
12/6/13 Virgil
12/7/13 wolfgang.mueckenheim@hs-augsburg.de
12/7/13 Virgil
12/4/13 Virgil
12/4/13 Tucsondrew@me.com
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Virgil
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 fom
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 fom
12/5/13 Tucsondrew@me.com
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Tucsondrew@me.com
12/5/13 Virgil
12/5/13 Virgil
12/5/13 Tucsondrew@me.com
12/5/13 fom
12/5/13 Tucsondrew@me.com
12/5/13 fom
12/5/13 Michael F. Stemper
12/5/13 fom
12/5/13 Tucsondrew@me.com
12/5/13 fom
12/6/13 wolfgang.mueckenheim@hs-augsburg.de
12/6/13 Tucsondrew@me.com
12/6/13 wolfgang.mueckenheim@hs-augsburg.de
12/6/13 Virgil
12/6/13 Virgil
12/6/13 Michael F. Stemper
12/6/13 wolfgang.mueckenheim@hs-augsburg.de
12/6/13 Virgil
12/7/13 albrecht
12/7/13 fom
12/7/13 albrecht
12/6/13 fom
12/7/13 wolfgang.mueckenheim@hs-augsburg.de
12/7/13 fom
12/7/13 Virgil
12/7/13 fom
12/8/13 Virgil
12/8/13 fom
12/6/13 fom
12/6/13 Virgil
12/6/13 fom
12/7/13 ross.finlayson@gmail.com
12/5/13 Tucsondrew@me.com
12/5/13 Tucsondrew@me.com
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Tucsondrew@me.com
12/5/13 Virgil
12/6/13 wolfgang.mueckenheim@hs-augsburg.de
12/6/13 Virgil
12/6/13 albrecht
12/6/13 wolfgang.mueckenheim@hs-augsburg.de
12/6/13 albrecht
12/6/13 Virgil
12/6/13 Tucsondrew@me.com
12/6/13 albrecht
12/6/13 albrecht
12/6/13 fom
12/6/13 Virgil
12/7/13 albrecht
12/8/13 albrecht
12/5/13 Virgil
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Virgil
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Virgil
12/5/13 Tucsondrew@me.com
12/4/13 Virgil
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Tucsondrew@me.com
12/5/13 wolfgang.mueckenheim@hs-augsburg.de
12/5/13 Virgil
12/6/13 wolfgang.mueckenheim@hs-augsburg.de
12/6/13 Virgil
12/5/13 Virgil
12/5/13 ross.finlayson@gmail.com
12/9/13 William Hughes
12/9/13 wolfgang.mueckenheim@hs-augsburg.de
12/9/13 William Hughes
12/9/13 wolfgang.mueckenheim@hs-augsburg.de
12/9/13 Tucsondrew@me.com
12/10/13 wolfgang.mueckenheim@hs-augsburg.de
12/10/13 Tucsondrew@me.com
12/10/13 wolfgang.mueckenheim@hs-augsburg.de
12/10/13 Virgil
12/10/13 Tucsondrew@me.com
12/10/13 Virgil
12/9/13 William Hughes
12/10/13 wolfgang.mueckenheim@hs-augsburg.de
12/10/13 William Hughes
12/10/13 wolfgang.mueckenheim@hs-augsburg.de
12/10/13 William Hughes
12/10/13 wolfgang.mueckenheim@hs-augsburg.de
12/10/13 William Hughes
12/10/13 Virgil
12/11/13 wolfgang.mueckenheim@hs-augsburg.de
12/11/13 Virgil
12/11/13 Tucsondrew@me.com
12/11/13 fom
12/11/13 Tucsondrew@me.com
12/11/13 William Hughes
12/11/13 wolfgang.mueckenheim@hs-augsburg.de
12/11/13 William Hughes
12/11/13 wolfgang.mueckenheim@hs-augsburg.de
12/11/13 William Hughes
12/11/13 Virgil
12/11/13 Virgil
12/11/13 fom
12/11/13 Virgil
12/13/13 albrecht
12/10/13 Virgil
12/10/13 wolfgang.mueckenheim@hs-augsburg.de
12/10/13 Virgil
12/10/13 Tucsondrew@me.com
12/11/13 wolfgang.mueckenheim@hs-augsburg.de
12/11/13 Virgil
12/11/13 Tucsondrew@me.com
12/11/13 wolfgang.mueckenheim@hs-augsburg.de
12/11/13 Tucsondrew@me.com
12/11/13 wolfgang.mueckenheim@hs-augsburg.de
12/11/13 Tucsondrew@me.com
12/12/13 wolfgang.mueckenheim@hs-augsburg.de
12/12/13 Tucsondrew@me.com
12/12/13 Virgil
12/12/13 Virgil
12/12/13 Virgil
12/12/13 Virgil
12/12/13 Virgil
12/11/13 fom
12/11/13 Virgil
12/12/13 wolfgang.mueckenheim@hs-augsburg.de
12/12/13 Virgil
12/11/13 Virgil
12/11/13 Virgil
12/10/13 Virgil
12/11/13 William Hughes
12/11/13 Virgil
12/11/13 William Hughes
12/11/13 Virgil
12/11/13 William Hughes
12/11/13 fom
12/11/13 Virgil
12/10/13 Virgil
12/9/13 Virgil
12/9/13 Tucsondrew@me.com
12/9/13 William Hughes
12/9/13 Tucsondrew@me.com
12/9/13 Virgil
12/9/13 William Hughes
12/9/13 Virgil
12/9/13 Tucsondrew@me.com
12/10/13 William Hughes