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Topic: Is (t^2-9)/(t-3) defined at t=3?
Replies: 166   Last Post: Oct 30, 2013 9:41 AM

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LudovicoVan

Posts: 3,201
From: London
Registered: 2/8/08
Re: Is (t^2-9)/(t-3) defined at t=3?
Posted: Sep 30, 2013 4:09 PM
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"Julio Di Egidio" <julio@diegidio.name> wrote in message
news:l2ckfj$m9s$1@dont-email.me...
> "Virgil" <virgil@ligriv.com> wrote in message
> news:virgil-523099.13365230092013@BIGNEWS.USENETMONSTER.COM...

>> In article <l2bb8m$3gt$1@dont-email.me>,
>> Robin Chapman <R.J.Chapman@ex.ac.uk> wrote:

>>> On 30/09/2013 07:58, Ciekaw wrote:
>>> > On Saturday, September 28, 2013 6:30:42 PM UTC+2, Hetware wrote:
>>> > >
>>> >> But F(t) is not defined at t=3 because it evaluates to 0/0.

>>> >
>>> > Hint L'Hôpital's rule
>>> >
>>> > f(t)=t-3
>>> > f'(t)=1
>>> >
>>> > lim[f(t)/f(t)]=lim[f'(t)/f'(t)]=lim[1/1]=1
>>> >
>>> > Analogy:
>>> > If x=0 then sin(x)/x = 1

>>>
>>> Hetware: 0/0 = 3
>>>
>>> Ciekaw: 0/0 = 1
>>>
>>> Any more entrants?

>>
>> How about 0/0 = NAN ?

>
> 0/0 = |R, i.e. the entire real line, in closed interval arithmetic.


That is incorrect: 0/0 = |R*, i.e. the entire *extended* real line, in
closed interval arithmetic. I think it could be the negative or positive
half of it if one considers signed zeros, but I barely remember the details
right now.

Julio




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9/28/13
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Hetware
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Michael F. Stemper
9/28/13
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Peter Percival
9/29/13
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quasi
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Richard Tobin
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10/6/13
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Hetware
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magidin@math.berkeley.edu
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Hetware
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LudovicoVan
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9/29/13
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Peter Percival
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Virgil
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Virgil
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10/13/13
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10/16/13
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10/16/13
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quasi
10/19/13
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Hetware
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quasi
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Hetware
10/20/13
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fom
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quasi
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Virgil
10/18/13
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Hetware
10/19/13
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10/19/13
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fom
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Peter Percival
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Hetware
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Hetware
10/19/13
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fom
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10/19/13
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Hetware
10/19/13
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10/20/13
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10/20/13
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