> On Oct 31, 5:39 pm, "Peter Webb" > <webbfamilyDIEspam...@optusnet.com.au> wrote: > > Graham Cooper wrote: > > > On Oct 31, 2:34 pm, "Peter Webb" > > > <webbfamilyDIEspam...@optusnet.com.au> wrote: > > > > Graham Cooper wrote: > > > > > On Oct 31, 1:37 pm, "Peter Webb" > > > > > <webbfamilyDIEspam...@optusnet.com.au> wrote: > > > > > > Graham Cooper wrote: > > > > > > > On Oct 30, 6:24 pm, "Peter Webb" wrote: > > > > > > > > > > You do claim to have a list of all Reals, don't you? > > > > > > > > > I have a listable set of all reals. > > > > > > > > > 0.000000.. 0.110000.. 0.111010.. 0.111110.. ... > > > > > > > 0.000111.. 0.101000.. 0.000010.. 0.001100.. ... > > > > > > > 0.111000.. 0.010010.. 0.001010.. 0.101010.. ... > > > > > > > 0.111100.. 0.001011.. 0.000011.. 0.111111.. ... > > > > > > > ... > > > > > > > > > > You haven't specified the list yet. > > > > > > > > > AHA! Peter is on the ball! > > > > > > > > > No enumeration function! Just a good ole countable SET of > > > > > > > all reals! > > > > > > > > > The order is arbitrary isn't it? > > > > > > > > > > > Otherwise your claim to prove anything given any > > > > > > > > > ENUMER-ABLE SET OF REALS clearly appears to have > > > > > > > > > failed on the set provided 5 times already. > > > > > > > > > > > Herc > > > > > > > > > > I made no such claim. To start off with, its nonsense. > > > > > > > > > Nonetheless it was the topic before you took over from > > > > > > > Moeblee. > > > > > > > > > On Oct 30, 9:18 am, MoeBlee <modem...@gmail.com> wrote: > > > > > > > > I just proved that given any enumerable set S of > > > > > > > > denumerable binary sequences there is denumerable > > > > > > > > binary sequence not in S. > > > > > > > > > If you do not wish to apply any mathematical approach to > > > > > > > the given countable set of reals, > > > > > > > > > 0.000000.. 0.110000.. 0.111010.. 0.111110.. ... > > > > > > > 0.000111.. 0.101000.. 0.000010.. 0.001100.. ... > > > > > > > 0.111000.. 0.010010.. 0.001010.. 0.101010.. ... > > > > > > > 0.111100.. 0.001011.. 0.000011.. 0.111111.. ... > > > > > > > ... > > > > > > > > That's not a given countable set of Reals. > > > > > > > > Its not even a list of a few Reals, or even a single Real. > > > > > > > > Lets start with the first Real on your list. Just the first > > > > > > one. I don't care about the others for the time being. What > > > > > > is the first Real on your list? > > > > > > > 0! Top left corner! > > > > > > OK, what is the second Real on the list? > > > > > > > Maybe you should DEFINE what you mean by countable set before > > > > > asking for one. > > > > > > You don't know what a countable set is? > > > > > > For the purposes of this thread, you can treat it as a set which > > > > can be bijected with N. > > > > > > Which means you have to specify which values in R correspond to > > > > which values in N. > > > > > > You have already told us that the Real corresponding to n=1 is > > > > 0. > > > > > > Now you can tell us the Real corresponding to n=2. > > > > > > Eventually you will need to specify the Reals corresponding to > > > > all natural numbers n, but I figure the values for n=1 (given) > > > > and n=2 (next) will be a good start. > > > > > This set can be bijected with N > > > > > 1/1 1/2 1/3 1/4 ... > > > 2/1 2/2 2/3 2/4 ... > > > 3/1 3/2 3/3 3/4 ... > > > 4/1 4/2 4/3 4/4 ... > > > ... > > > > Yes. > > > > > > > > > similarly this set of reals CAN-BE bijected with N > > > > > 0.000000.. 0.110000.. 0.111010.. 0.111110.. ... > > > 0.000111.. 0.101000.. 0.000010.. 0.001100.. ... > > > 0.111000.. 0.010010.. 0.001010.. 0.101010.. ... > > > 0.111100.. 0.001011.. 0.000011.. 0.111111.. ... > > > ... > > > > But this isn't a list of Reals. > > > > It is a list of the first few decimal digits of a few unspecified > > Reals. > > > > You need to produce a list of Reals. > > > > Lets do this in steps. > > > > What is the second Real on your list? > > > > > > > > > Hence, you CANNOT prove a COUNTABLE SET OF REALS is incomplete. > > > > > PROOF: This is the 10th time asking. > > > > > In fact, I call this THE UNANSWERABLE QUESTION for a reason! > > > > > Herc > > > > And the second Real on your list is? > > OK use this countable set of reals. > > 1/10 1/20 1/30 1/40 ... > 2/11 2/21 2/31 2/41 ... > 3/31 3/32 3/33 3/34 ... > 4/17 4/27 4/37 4/47 ... > ... > > what's missing? > > Herc
pi - 3
So your list of all Reals is missing pi - 3. Turned out it wasn't a list of all Reals after all.
So at least that is cleared up; you now know your list of all Reals doesn't include all Reals you can stop going on about it.
