On Fri, Dec 09, 2022 at 09:38:25PM +0100, Michael Heerdegen wrote: > writes: > > > My choice was school maths [...] [...] > Or you remember how e can be introduced: with > > / 1\ n / 1\ n+1 > a_n := |1 + -| and b_n := |1 + -| > \ n/ \ n/ FWIW, I started with the binomial formula, (1000 + 1)^1000 = 1000^1000 + (n-over-1) * 1000^999 + ... Now n-over-1 is 1000, so we already have a 2 at the left (more to come, of course :) Next (n-over-2) is 1000*999/1*2 (so roughly 1000*1000/2, that adds 0.5 to the most significant, that makes 25...; Next 1000^3/6, so we are at 2666... The denominator grows quickly (a tad more than an exponential), so things are bound to converge quickly; besides, I over-estimated things by setting 99x to 1000. That already started looking a lot like e. Then I remembered that limit I quoted from you above. Then I asked Guile and Emacs. Cheers -- t