RE : inf - inf = 0 ??




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From: "Richard Hennessy" <rich.hennessy at verizon.net>
Sent: Thursday, September 09, 2010 5:00 PM
To: <maxima at math.utexas.edu>
Subject: Re: [Maxima] RE :  inf - inf = 0 ??

>
>
> --------------------------------------------------
> From: "Richard Fateman" <fateman at cs.berkeley.edu>
> Sent: Thursday, September 09, 2010 10:12 AM
> To: "Dan" <vi5u0-maxima at yahoo.co.uk>
> Cc: "Maxima mailing list" <maxima at math.utexas.edu>
> Subject: Re: [Maxima] RE :  inf - inf = 0 ??
>
>>  On 9/9/2010 3:46 AM, Dan wrote:
>>> On Wed, 8 Sep 2010, Richard Hennessy wrote:
>>>
>>>> Yes, it does mean that.  limit(expr1,x,a)-limit(expr2,x,a) is not always equal to limit(expr1-expr2,x,a);
>>>
>>> According to my notes on Erd?lyi (1956, _Asymptotic expansions_, Dover
>>> Publications, New York, pp. 14-15), a linear combination of asymptotic
>>> expansions of two functions is an asymptotic expansion of the same
>>> linear combination of the two functions.  The same point appears in my
>>> notes on Hinch (1991, _Perturbation methods_, Cambridge University
>>> Press, Cambridge, p. 22).  A limit has to be asymptotic to the thing
>>> it's the limit of, no?
>> no.
>>
> I think they say in the theorems on limits "if the limits exist", so it is not unconditionally true.  So limit(a) may 
> not exist which sometimes means it is inf or minf or unsigned infinity or complex infinity or ind.  Consider 
> limit(cos(x)^2 + sin(x^2), x ,inf);

I meant consider
limit(cos(x)^2 + sin(x)^2, x ,inf);

>
>
>>> How does all this sit together?
>> read about limits, instead. I think you will find that
>>
>> lim(a+b) = lim(a)+lim(b)  if  lim(a) and lim(b) are finite, or at least one of them is finite.
>>
>> RJF
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