In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 25 Okt., 21:41, SPQR <S...@roman.gov> wrote: > > > d_1, d_2, d_3, ..., d_oo > l_1, l_2, l_3, ..., l_oo > b_1, b_2, b_3, ... > > > > The you deny that the sequences include their limit ordinal omega? You > > > deny that each of both sequences has a limit sequence with aleph_0 > > > elements? > > > > Yes and No! I deny that any sequence of finite naturals includes > > anything other than finite naturals, > > Hence you deny that the sequences above include d_oo or l_oo.
The first two are not, strictly speaking sequences at all because they both contain more than one element without any immediate predecessor, and sequences do not allow that, at least outside of WM's matheological but illogical world. > > > > but not that such infinite > > sequences can contain aleph_0 distinct elements. > > That is not the question here.
It is a part of the questions that you asked above.
> Of course. Whether aleph_0 has any meaning is under discussion. > Whether a sequence indexed by naturals can include oo has been settled > now: It cannot.
No set of naturals, whether members of a sequence or not, can contain a non-natural like aleph_0. But that does not eliminate having a set of all naturals, whether regarded as an ordered set of not.
Such as in ZFC. And other parts of standard mathematics, and regardless of WM's attempts to impose his matheology on mathematics.
Therefore the sequence (d_n) cannot include d_oo. > > > Regards, WM