Timeline for How can I make 1+$MachineEpsilon not look like 1?
Current License: CC BY-SA 3.0
6 events
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| Apr 13, 2017 at 12:56 | history | edited | CommunityBot |
replaced http://mathematica.stackexchange.com/ with https://mathematica.stackexchange.com/
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| Dec 13, 2015 at 10:47 | history | edited | Michael E2 | CC BY-SA 3.0 |
Fixed typo
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| Jan 12, 2015 at 2:46 | comment | added | Michael E2 |
@gaazkam The precision of 1 + $MachineEpsilon is MachinePrecision, so SetPrecision[1 + $MachineEpsilon, MachinePrecision] does nothing. SetPrecision[x, $MachinePrecision] almost works, but not quite, because 1 + $MachineEpsilon is a little bigger than 1. You could get by with $MachinePrecision + 0.1. It's a bit complicated for a comment, but machine numbers are represented with a finite number of bits and the notion of Precision is relative to the size of x. There are discrete jumps in precision when the exponent changes. N[x, 100] won't increase the precision of x.
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| Jan 12, 2015 at 1:54 | comment | added | gaazkam |
Many thanks, it works! BTW: SetPrecision[1 + $MachineEpsilon, MachinePrecision + 1] gives 1.0000000000000002, as it should; but SetPrecision[1 + $MachineEpsilon, MachinePrecision] gives 1. Why? 1+$MachineEpsilon is a machine number, so why can't it be displayed with machine precision? And why does N[1 + $MachineEpsilon, 100] still give 1.?
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| Jan 12, 2015 at 1:48 | vote | accept | gaazkam | ||
| Jan 12, 2015 at 1:12 | history | answered | Michael E2 | CC BY-SA 3.0 |