In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 13 Jul., 21:47, Virgil <vir...@ligriv.com> wrote: > > In article > > <fbaaf5f9-8368-423a-ab22-0155da82b...@v9g2000vbc.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 13 Jul., 10:17, Virgil <vir...@ligriv.com> wrote: > > > > > > On the contrary, in STANDARD mathematics, the arguments of a function > > > > need not be numbers at all, but can be members of any set at all. > > > > > In standard mathematics, the limit of the sequence (1/n) is 0 and only > > > 0. > > > > But a function discontinuous at each -1/n, as is the case here, need not > > be continuous at 0. > > In mathematics, the sequence a_n = 1/n has the limit 0. Continuity is > nor required. Sequences in general are discontinuous. But I teach my > students how limits can be calculated. Should that all be nonsense on > behalf of some matheologians who otherwise had to confess that they > have been following some not very important occupation? > > > > The actual number of balls in the VASE function of time in seconds is > > 0 for t < -1, > > 9*n for -1/n <= t < -1/(n+1) > > for all times before 0, so is increasingly discontinuous at each > > t = -1/n ( the discontinuities keep getting larger as n increases), > > a set of values converging to 0. > > > > But now WM claims, as usual without proof, that that function MUST be > > 'sort of continuous' at an accumulation point of its discontinuities. > > Mathematics gives the improper limit oo. > Set theory gives the limit 0. > What would you believe to be correct?
The proper VALUE at t = 0 is the number of balls which have been inserted into the vase but not removed, but since every ball entered has been removed, that must be 0. > > You see here: WMatheology requires belief. Mathematics does not.
WM's WMatheology requires violating the statement of the original problem, standard mathematics does not. --