Suppose we divide the the interval $[0,1]$ into $t$ equal intervals labeled $i_1$ upto $i_t$, then we make a function $f(t,x)$ that returns $1$ if $x$ is in $i_n$ and $n$ is odd, and $0$ if $n$ is even.
What is $\lim_{t \rightarrow \infty} f(t,1/3)$?
What is $\lim_{t \rightarrow \infty} f(t,1/2)$?
What is $\lim_{t \rightarrow \infty} f(t,1/\pi)$?
What is $\lim_{t \rightarrow \infty} f(t,x)$?
joriki clarification in comments is correct, does $\lim_{t \rightarrow \infty} f(t,1/\pi)$ exist, is it 0 or 1 or (0 or 1) or undefined? Is it incorrect to say that is (0 or 1)?
Is there a way to express this:
$K=\lim_{t \rightarrow \infty} f(t,x)$
K, without limit operator ?
I think to say K is simply undefined is an easy way out. Something undefined cant have properties. Does K have any properties? Is K a concept?