In article <email@example.com>, WM <firstname.lastname@example.org> 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.
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. --