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SetPrecision - What does in find?
Let us run SetPrecision[.14, \[Infinity]] MATHEMATICA returns 1261007895663739/9007199254740992. What is the mathematical (in the sens of mathemaics as a science) reason to give this answer? I would say that 7/50 is much a better answer. It looks like that the MATHEMATICA's (in the sens of rules of MATHEMATICA) reason 1261007895663739/9007199254740992 can be observed by the command N[1261007895663739/9007199254740992, 100] which answers .14000000000000001332267629550187848508358001708984375000000 00000000000000000000000000000000000000000 It puts 14 zeros after .14 to coinside with 14/100 within the machine precision which is about 16, than it puts an arbitrary number and than it puts zeros again. It looks that the number is the exact presentation of the fractoin 1261007895663739/9007199254740992, but it is not exactly .14, the deviation being the machine precission. MATHEMATICA tries to find a fraction which has a finit digital presentation, but which defers from the .14 by a michine precision. Is there a meaning to obtaing a number like this?