PDF: the height is a density, the area is a probability

Companion demo for math-foundations §1. Drag the width slider toward 0: the shaded probability collapses to nothing, while the curve's height barely moves. That gap is the whole PMF-vs-PDF distinction — for a continuous variable you measure an area, never a height.

height = density p(x)
0.242
per unit x · stays fixed
window width Δx
1.00
drag the slider
P = shaded area
0.242
→ 0 as Δx → 0
1.0
1.00