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Re: More /.{I->-1} craziness. Schools
*To*: mathgroup at smc.vnet.net
*Subject*: [mg106940] Re: More /.{I->-1} craziness. Schools
*From*: Richard Fateman <fateman at cs.berkeley.edu>
*Date*: Fri, 29 Jan 2010 07:45:13 -0500 (EST)
*References*: <hjbvc0$2tp$1@smc.vnet.net> <hjeqh1$g3c$1@smc.vnet.net> <hjh877$r4r$1@smc.vnet.net> <201001261133.GAA00712@smc.vnet.net> <201001270644.BAA04729@smc.vnet.net> <op.u67uiib3tgfoz2@bobbys-imac.local> <hjrf98$n1e$1@smc.vnet.net>
Daniel Lichtblau wrote:
...
>
> One implication is that a "zero" of sufficiently low (as in bad)
> accuracy can be regarded as 1, or -1, or Pi, if those values happen to
> fall within the accuracy (which I refer to as fuzz).
>
> The other inequalities follow from the preservation of trichotomy. For
> explicitly real values we regard that as important. mathematica makes no
> pretense that Equal is transitive and I do not see any way to do that
> and also have useful approximate arithmetic.
>
If you insist on equality meaning "overlap", then maybe you should give
up on trichotomy for fuzz-balls, since its preservation leads to
nonsense. That is, if x==0 and x==1 and x==2, on the grounds that the
fuzzball for x includes 0,1,2, and x might "possibly be equal" to 0, 1,
or 2, then doesn't it follow that x<1 and x>1 are also "possible", and
therefore these are true too?
In the interval arithmetic world these would be called 'possibly equal',
'possibly greater than' 'possibly less than' etc.
As opposed to the more usual 'certainly equal' etc.
RJF
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