On Mon, 9 Nov 2015 04:21:14 -0800 (PST), Salvatore DI DIO wrote: > > I was trying to show that this limit was 'e' > But when I try large numbers I get errors > > def lim(p): > return math.pow(1 + 1.0 / p , p) > >>>> lim(500000000) > 2.718281748862504 >>>> lim(900000000) > 2.7182820518605446 !!!!
Python floats have close to 16 decimal digits of precision. When you compute 1+1/p with large p, the result will be close to 1, so digits of 1/p beyond the 16th place will be damaged by rounding. For p of 900000000, the first nearly-9 digits of 1/p are zero, so the first "significant" digit is the 10th, and beyond the 16th digit -- the 7th significant digit -- they're damaged, so you can only expect about 16-9 = 7 significant digits to be accurate. And as it turns out, 2.7182820518605446 is good to about 7 significant figures. It takes longer to explain than to see: roundoff limits you to ... (digits of p) + (good digits in the result) = 16 (approximately) -- To email me, substitute nowhere->runbox, invalid->com. -- https://mail.python.org/mailman/listinfo/python-list
