10 Dec
2018
10 Dec
'18
3:43 p.m.
There is the greedy-harmonic-series-with-signs method: Let C be the irrational real number to approximate; say C > 0. Then let p1 be the least integer for which 1 + 1/2 + 1/3 + ... + 1/p1 > C. Now let n1 be the least integer > p1 for which 1 + 1/2 + 1/3 + ... + 1/p1 - (1/(p1+1) + 1/(p1+2) + ... + 1/n1) < C Continue this way, alternately adding and subtracting groups of consecutive terms, resulting in a signed harmonic series that converges to C. —Dan Keith Lynch wrote: ----- ..... What are some exotic ways to approximate real numbers to any desired precision? Extra points if you can come up with something completely original. -----