← Math Intuition Labs

Number Systems Explorer

Integers, rationals, irrationals — and the gaps between them

Pan and zoom along the number line. Toggle layers to see integers (discrete lattice), rationals (dense but holey), and famous irrationals. Zoom in to watch rationals multiply; zoom out to see structure emerge.

window: [-4.00, 6.00]integers visible: 11rationals visible: 110irrationals visible: 7
ZQR\Q-4-3-2-10123456-4-3-2-10123456√2πeφ√3√5ln2

Zoom in to see rationals become denser — between any two, infinitely more exist.

Yet irrationals fill the "gaps" that rationals leave. The reals complete the line; the rationals alone cannot.

Number Systems Explorer — Math Intuition Labs · hbar.university