Re: continuity of norm function in R^n
From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 08/02/04
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Date: Mon, 02 Aug 2004 15:59:44 -0500
On 2 Aug 2004 12:39:57 -0700, frank.degeeter@skynet.be (Frank De
Geeter) wrote:
>David C. Ullrich <ullrich@math.okstate.edu> wrote in message news:<ic5qg09jcdu4t2qiqu70qf8ogpbn3nhmsp@4ax.com>...
>> On 1 Aug 2004 06:51:08 -0700, frank.degeeter@skynet.be (Frank De
>> Geeter) wrote:
>>
>> >Hi,
>> >
>> >I am trying to study analysis on my own, using SA Douglass'
>> >Mathematical Analysis. Marvelous textbook, but a hard job
>> >nevertheless. From time to time I get stuck. I am now.
>> >On page 124 the text states that "evidently f(x)=||x|| is continuous
>> >for all c in R^n". That seems entirely plausible indeed to me, but I
>> >tried to devise a proof based on the epsilon-delta definition of
>> >continuity. That did not work out well, however. Anyone out there who
>> >would care to get me back on the track?
>>
>> if you want to get back on track you should -read- the replies
>> to your -previous- posts!
>>
>> i mean really - because i'm typing one-handed right now it actually
>> took me several minutes to type the inequality in my previous reply.
>> you'd prefer i do that again, so you can ignore -this- reply and
>> post the question a fourth time?
>>
>Sorry about the triple posting. I am new to this discussion group
>thing and I could not find the message I posted,
oh. i assumed that you just wanted someone to work out all the
details and intended to keep posting til you got a reply that
didn't require any work on your part. sorry.
dunno how you could be unable to find your post. i see
you're using google groups. a lot of people prefer a
'real' news reader - go to
http://www.forteinc.com/main/homepage.php
and get a free copy of Agent. then you also need a news
server. your isp may have one, or you could google
'news server' and find free ones and commercial ones
[if you want extreme reliability for a small fee
try giganews]
>so I decided to redo
>it, and again. Since I found it now I'll save you that fourth posting.
>If in the mean time I could do something else to hasten your recovery,
>please tell me - I happen to be a physician
it's just a cracked shoulder - the er guy said he didn't see
the point to anything other than just putting the arm in a sling
and waiting for it to get better. first few days i decided he was
a sadistic incompetent lunatic, but as of the last few days it seems
he may be right, i doubt you can add much, unless your field is
like nuclear medicine or something...
>(although my field is nuclear medicine, really).
keen. i've read that if i take a few milligrams of plutonium my
pain will go away in at most a few days. been wondering where
to go for a second opinion... [plutonium isn't addictive, is it?]
>Many thanks for your answer to my question. I had indeed sought after
>this type of inequality, but I did not know it held true in R^n. Now
>that you mention it, I find no difficulty in proving it - but my
>textbook did not mention it on the previous pages. Anyway, you
>single-armed got me back on track!Thanks.
>
>Frank
************************
David C. Ullrich
sorry about the inelegant formatting - typing
one-handed for a few weeks...
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