Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 wolfgang.mueckenheim@hs-augsburg.de Posts: 3,394 Registered: 10/18/08
Re: Matheology 400: Quantifier Confusion
Posted: Dec 7, 2013 4:44 AM

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.
>
>
>

> > 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.
>
> 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.
>
>
>
> Such a Mastery of Logic, Dear Professor!

You see, as usual you have only failed to understand.
>

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

I do not reject AoT but the interpretation of set that is unjustufied because "set" has no definition.
>
> But, you do more than that. You claim that its acceptance must and will lead to a Contradiction.

>
>
>
> 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.

> They never when around to their contemporaries screaming, "You're using an inconsistent system!".

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

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.

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.
>
You are a Crank!
>
>
>

> > > 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?
>
>
>
> 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.
>

> > I can see why your logic has nothing to do with mathematics, simply because you cannot take all.

>
> Purely Philosophical Grounds.

Not at all. Mathematics (AoI) shows: Every n is followed by infinitely many.
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.

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

> > > Percentages are non-sensical in this context unless more rigorously defined.
>
> >
>
> > Perhaps you cannot understand that every finite number is less than 1/100 of aleph_0?
>
>
>
> Beep, Beep, Beep.

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

REgards, WM

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