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Re: Re: confused about == vs === in this equality
*To*: mathgroup at smc.vnet.net
*Subject*: [mg103777] Re: [mg103750] Re: [mg103732] confused about == vs === in this equality
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Mon, 5 Oct 2009 13:17:29 -0400 (EDT)
*References*: <20091003104738.LCJ3I.416659.imail@eastrmwml34> <200910051136.HAA28533@smc.vnet.net>
On 5 Oct 2009, at 20:36, danl at wolfram.com wrote:
> he decision, which I believe only goes back a few versions, was to
> also
> treat infinities in that way. From a mathematical point of view this
> makes
> sense, and it may well be useful in the innards of some Limit code in
> avoiding what would be incorrect cancellations. (Though I have
> worked on
> that code, I do not recall all specifics, but I think we always
> carefully
> guarded against this.)
This does not seem to be quite true, at least not for all infinities.
Infinity == Infinity
True
I think this is reasonable as in a certain sense there is "only one"
positive real infinity. Similarly:
DirectedInfinity[I] == DirectedInfinity[I]
True
and so on. So, I think, as I wrote in my other message in this thread,
it is probably the case that DirectiedInfinity[] and Indeterminate are
the only symbols with this property.
I completely agree with the behaviour of Indeterminate but still have
some doubts about DirectedInfinity[] and would like to see an example
where having equality return true would cause some sort of problem or
weirdness.
Andrzej Kozlowski
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