>>11955857

>convergence of functions, even uniform, doesn't imply convergence of derivatives

That's right. Therefore you CAN'T assume that a series such as:

.9

.99

.999

.9999

.99999

...will have 1 as its conclusion. There simply is no "conclusion" to this, just like there is no "last nine" at the end of .999...

Pictured: Line BW has a slope of 0. Line BZ has an infinitesimal slope. They are clearly different lines that arrive at different points, and only intersect at 0,0.