Re: Re: More /.{I->-1} craziness. Schools are conservative.

• To: mathgroup at smc.vnet.net
• Subject: [mg106656] Re: [mg106882] Re: More /.{I->-1} craziness. Schools are conservative.
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Wed, 27 Jan 2010 01:44:22 -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>

```Richard Fateman wrote:
> [...]
> If all of Mathematica functionality were available in the free player
> version, WRI would need to drastically change its business model. And
> even it it were free, we still have behavior like this: (..for some
> values of zero)
>
>    {x >== 1, x > 0, x}  evaluates to {True, False, 0.}
>
> RJF

Let's take simple intervals, that is, intervals that are segments.
Define less and greater in the obvious ways, that is, one segment lies
strictly below the other (right endpoint of lesser is less than left
endpoint of larger). Let us further define two intervals to be equal
whenever they have nonempty intersection.

With these definitions, which I think are sensible, the behavior you
describe above is consistent with arithmetic on intervals. As the
numbers involved, at least some of them, are fuzzballs, this strikes me
as an appropriate behavior.

Daniel Lichtblau
Wolfram Research

```

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