In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 15 Jun., 21:11, "Mike Terry" > <news.dead.person.sto...@darjeeling.plus.com> wrote: > > > > 1) What you write is sloppy (mathematically) and so it's not > > clear what you intend to say with your individual statements. > > But actually everybody can easily imagine what is meant.
Quite often not.
> You prove it > for your person below. > > > > > > Consider the list of increasing lengths of finite prefixes of pi > > > > > 3 > > > 31 > > > 314 > > > 3141 > > > .... > > > > > Everyone agrees that: > > > this list contains every digit of pi (1) > > > > Literally this just doesn't make sense. > > Obviously he means that this list contains every digit of pi with the > correct index enumerating its position. In discussions like the > present one it is not usual to state everything explicitly that can be > understood by an experienced reader. > > > Perhaps you mean to say: > > > > this list contains every finite prefix of the infinite > > digit sequence for pi (1)? > > > > I would agree with that... > > > > (What you actually said is gibberish because the list is not a list of > > digits. If we try to treat it as such, then the only digit in the list is > > 3). > > A list of people can contain and usually does contain letters.
A list of people should contain only people. A list of people's names can contain and usually does contain letters, other than in, say, Chinese or Japanese.
> Thiks list is not a set in orthodox set theory. > > > > > [My suspicion at this point is that your gibberish wording is actually the > > *key* in some way to how you want to introduce some incorrect conclusion, > > but time will tell on that. If I'm right, you won't like my clarification, > > because it will make it harder for you to express your mistake...] > > This suspicion is wrong. > > Every initial segment of the decimal expansion of pi is in at least > one line of your list > 3. > 3.1 > 3.14 > 3.141 > ...
Actually, in all but finitely many of those lines.
> What we can find in the diagonal, namely 3.141 and so on, exactly that > can be found in one line. This is obvious by construction of the > list.
That is FALSE, since the "diagonal" is necessarily endless and each line ends.
> So consider this: > > Every part of the diagonal is in at least one line.
Each finite initial part, but not any non-empty terminal part.
> That means That means WM is wrong. me. > > The latter proposition can be excluded. If there are more than one > lines that contain parts of pi, then it can be proved, be induction, > that two of them contain the same as one of them. This can be extended > to three lines and four lines and so on for every initial segment of n > lines.
Every FINITE initial segment, but each of those omits more than it inlcudes. > > Hence we prove that all of pi, that is contained in at least one of > the finite lines of this list, is contained in one single line.
Only if there is a last line, which there is not. > > Conclusion: Either the complete diagonal pi does not exist, or it > exists also in one and the same single line (because every line that > can contain a digit sequence, is a finite line).
Conclusion false, as it requires the existence of a last line, which does not occur.
If one has a (finite) last line, one does not have pi. And if one does not have a last line, WM's argument fails.