Author Archives: Paul Crowley

Very big numbers like Graham’s Number are often expressed with lengthy, clumsy, semi formal explanations. But it’s concise and convenient to express such numbers precisely in the pure lambda calculus, using Church numerals. Starting with Knuth’s up-arrow, if we define fn,a(b) = a↑nb, then f0,a(b) = ab and fn+1,a(b) = fn,ab(1). From this we get thatContinue reading “Lambda calculus and Graham’s number”