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Re: Motion P1788/M003.01_Set_of_reals

Michel Hack schrieb:

In response to Ian McIntosh's NO vote, Jõrgen Wolff v Gudenberg
revised his initial comment [...] and wrote:


This may seem to give more information.  But actually the value
of log(0) is not defined.  Hence the result is the empty set.


I think Ian's point was that 754-2008 defines log(0) to be -oo, just
like -1/0  (or, for that matter, 1/-0).  In either case the DivByZero
flag is set (if not trapped) -- precisely because 754 operates in R*.
The purpose of standard interval arithmetic is not to enclose the results of IEEE-754 arithmetic, but to enclose the results of ideal 
real arithmetic. Thus it is immaterial how IEEE-754 defines log(0).

In the ideal world of mathematics, log(0) is undefined.


Arnold Neumaier