mfb
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TIL how well you can approximate e ##\approx## 2.718281828 with a few basic symbols and numbers 1 to n:
##2^{(.3+.1)^{–.4}–5^{–7.6}}##, using 1 to 7, has an error of –1.57*10-8
##(1+2^{–76})^{4^{38}+.5}##, using 1 to 8, has an error of 3.96*10-47
##\displaystyle \left(1+9^{-4^{7\cdot 6}} \right)^{3^{2^{85}}}##, using 1 to 9, has an error of –2.01*10-18,457,734,525,360,901,453,873,570. If you write its decimal digits in 10 micrometer small letters and cover the whole surface of Earth with digits, all digits will be correct.
http://www2.stetson.edu/~efriedma/mathmagic/0804.html
##2^{(.3+.1)^{–.4}–5^{–7.6}}##, using 1 to 7, has an error of –1.57*10-8
##(1+2^{–76})^{4^{38}+.5}##, using 1 to 8, has an error of 3.96*10-47
##\displaystyle \left(1+9^{-4^{7\cdot 6}} \right)^{3^{2^{85}}}##, using 1 to 9, has an error of –2.01*10-18,457,734,525,360,901,453,873,570. If you write its decimal digits in 10 micrometer small letters and cover the whole surface of Earth with digits, all digits will be correct.
http://www2.stetson.edu/~efriedma/mathmagic/0804.html