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.
