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Re: [Axiom-developer] [Bug?] "error in library; negative log"

From: Bob McElrath
Subject: Re: [Axiom-developer] [Bug?] "error in library; negative log"
Date: Fri, 11 Nov 2005 22:13:51 -0800
User-agent: Mutt/1.5.11

(-1)^\infty is an indeterminate expression, like 0/0.

Mathematica returns Indeterminate, and maple returns "-1 .. 1" since the
limit is bounded, but indeterminate on the interval [-1,1].

Infinity is neither even nor odd.

Karl Hegbloom address@hidden wrote:
> Attached is a session log showing an error that I receive while
> attempting to produce a sequence from an expression in Axiom.  Maxima
> seems to have no trouble with the similar expression, and computing the
> value of the expression by hand, as you can see, seems to work fine
> also.
> Another problem I have is that taking the limit of an expression
> containing (-1)^n always returns "failed", where my TI-89 Titanium
> calculator will give a finite limit.  For example:
>  limit( 2 + (-2/%pi)^n, n=%plusInfinity )  ===> "failed"
> ... but the TI-89t returns 2.
> The TI-89t says that the limit of (-1)^n as n approaches infinity is -1,
> implying that it believes that infinity is an odd number.  That kind of
> makes sense to me, since if you divide infinity in half, you still have
> infinity, and you keep adding 1 to get to infinity, making it odd.  If
> infinity is even then the answer should be 1, and if we can't know if
> infinity is even or odd, then the answer is uncertain or undefined.
> On the other hand, the TI-89t says that lim ( (-1)^n * (n + 1)/n ) is
> undefined.  But it already told me that lim (-1)^n = -1, and that lim (n
> + 1)/n = 1.  If the limit of a product is the product of the limits of
> the factors, then lim ( (-1)^n * (n + 1)/n ) should be -1, right?
> So, who's right?

Bob McElrath [Univ. of California at Davis, Department of Physics]

    "In science, 'fact' can only mean 'confirmed to such a degree that it would
    be perverse to withhold provisional assent.' I suppose that apples might
    start to rise tomorrow, but the possibility does not merit equal time in
    physics classrooms." -- Stephen Jay Gould (1941 - 2002)

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