On 3/30/2013 8:34 AM, WM wrote: > On 29 Mrz., 19:40, Virgil <vir...@ligriv.com> wrote: >> In article >> <ce3c22f2-9116-4621-b3b4-e722fe51a...@a14g2000vbm.googlegroups.com>, >> >> WM <mueck...@rz.fh-augsburg.de> wrote: >>> On 26 Mrz., 22:47, Virgil <vir...@ligriv.com> wrote: >> >>>> But a tree that contains paths for all binary rationals will contain a >>>> path for all limits of a sequences of binary rationals. >> >>> Does a sequence always contain its limit? >> >> Depends on the sequence, of course. but a sequence of paths in a >> Complete Infinite Binary Tree in which the nth path must share at least >> n nodes with each of its successors will always converge, though not >> neccessarily to a binary rational. > > A sequence of numbers may converge, but not necessarily to a limit > that is a term of the sequence. > A sequence of paths may converge, but not necessarily to a limit that > is a term of the sequence.
Genus: convergent sequences of ground objects
Species: convergent sequences of ground objects having a ground object as a limit
Coordinate Species: convergent sequences of ground objects not having a ground object as a limit
Define an identity criterion for congruence classes of convergent sequences of ground objects
Define an arithmetical calculus for congruence classes of convergent sequences of ground objects
> If you believe in a difference between numbers and paths, you should > be able to substantiate that belief. But you cannot reason with > mathematical arguments. Again you have to believe in matheology as the > "reason" of this difference. > > In mathematics more precision is required. >
That is the point everyone has been making to WM.
But, then, there is no arguing with a religious zealot.