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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

• References:
  • Re: confused about == vs === in this equality
    • From: danl@wolfram.com