import graph;
usepackage("amsfonts");

size(10cm, 10cm, IgnoreAspect);

side further = Relative(N);

int till = 12;

xaxis(Label("$n \in \mathbb N$", 6further), 0, till + 0.9, Ticks(Step = 1, modify = NoZero), Arrow);
yaxis(Label("$a_n \in \mathbb R$", 3further), 0, 1.15, Ticks(Step = 1, modify = NoZero), Arrow, autorotate = false);
label("0", (0, 0), SW);

real a(int n) {return n % 2 == 1 ? 1 / n : 1;}

pen toggle (int n) {return n % 2 == 1 ? red : blue;}

for (int n = 0; n <= till; ++n)
	dot((n, a(n)), toggle(n) + 6);

shipout("Subsequential limit (vs limit point)");

erase();
size(0, 10cm);
// Either erase() or (re)size gets automatic scaling disabled, consequently, Ticks(N = ...) works no more

yaxis(Label("$\left\{\, a_n \in \mathbb R  \,\middle|\, n \in \mathbb N \,\right\}$", 3further), 0, 1.1, Ticks(Step = 1), Arrow, autorotate = false);

pen toggle2 (int n) {
	pen p = toggle(n);
	real w = linewidth(p);
	return n  == 1 ? p = p + (w + 6) : p;}

for (int n = 0; n <= 1000; ++n)
	dot((0, a(n)), toggle2(n));

shipout("Limit point (vs subsequential limit)");