/SQTDDTOT/ IS DEAD

It is n minus the multiples of k that are less than n.
Euclidean division: n=qk+r
It is n-q.

Oh wait, add 1 cause you could have one element that can be divided by k if n is greater or equal to k.
n-q+1

How does it handle this day in and day out? How does it not dig itself through?

...

Any able to help with some metric spaces business

Two things you can try:
1) Compute the distance between fn and fm for arbitrary n and m. Is that compatible with a convergent sequence?

2) For which x does the sequence converge pointwise? Do you know any results relating pointwise convergence and convergence with respect the sup norm?

Check out [math] d(f_{n+1} ,f_n) [/math]
You will find out that it's not converging to 0

>to 0
The question is whether it converges to 1/x not 0 and it doesn't.

i'm talking about the metric converging to 0 not the function

Suppose that f_n converges uniformly against a function f then f must also be equal to the pointwise limit.

[eqn]\lim_{n \to \infty} f_n(x) = \begin{cases} 0 & \text{if } x = 0 \\ \frac{1}{x} & \text{else } \end{cases} [/eqn]

but [math] f(x) = \begin{cases} 0 & \text{if } x = 0 \\ \frac{1}{x} & \text{else} \end{cases} \not \in C([0,1]) [/math].