Demos

Programs that demonstrate omega's infinite values, plus a Mandelbrot renderer. They assume ordinals and cardinals.

count

Counts through the finite numbers and on past them: omega, omega plus one, omega squared, towers of omegas, epsilon0 and finally omega1, whose cardinality is aleph1. It ends with the continuum hypothesis.

ord-demo

Ordinal and cardinal arithmetic, one line at a time. 1 + w = w next to w + 1 = w+1 shows that ordinal addition isn't commutative.

pairing

Pairs the natural numbers with the even numbers one to one, showing that both sets have the same size.

diagonal

Cantor's diagonal argument. It flips the diagonal of a list of binary rows to build a row that can't appear in the list, proving that 2 aleph0 ^ is larger than aleph0.

supertask

Halves a line repeatedly until the screen runs out of resolution, illustrating infinitely many steps with a finite total.

powerset

[ 1 2 ] powerset .

Returns every subset of a list. n items give 2^n subsets.

mandel

The Mandelbrot set in text mode, zooming in on each key press. It uses fixed point with 65536 as 1.0. mandel-at draws a single view:

-32768 0 2816 40 mandel-at

Its inner loop, mb-iter, is almost pure arithmetic, which is where the JIT helps most. 'mb-iter xray shows the compiled code.

The demos are short, and 'count see or 'diagonal see show real code using the ordinal words.