Free public beta until December 4, 2026: every course is open, no card needed. After that, the first chapter of each course stays free and full access is a one-time $39 ($19 for up to 100 founding members chosen for helpful feedback). Your progress is kept. How the beta works

typical set

The (relatively small) set of length-n sequences a source is overwhelmingly likely to actually produce, each occurring with probability close to $2^{-nH(X)}$ .

The AEP bounds the typical set's size, $(1-\varepsilon)2^{n(H-\varepsilon)} \leq |A_\varepsilon^{(n)}| \leq 2^{n(H+\varepsilon)}$ , vanishingly small compared to the full $2^n$ possible sequences whenever $H(X)<1$ .

Read the full section →

snap pen only

Graph settings

indep dep deg

grid intersections

xmin xmax ymin ymax

x-tick y-tick

Calculator