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RE: KISS-decorations

Oops, yes, I goofed, it is continuous on this interval :-(

________________________________________
From: Corliss, George [george.corliss@xxxxxxxxxxxxx]
Sent: Saturday, July 02, 2011 8:21 AM
To: Kreinovich, Vladik
Cc: Corliss, George; Nate Hayes; Jürgen Wolff von Gudenberg; John Pryce; Dominique Lohez; stds-1788@xxxxxxxx
Subject: Re: KISS-decorations

Vladik,

Did you look at the interval argument before you made your comment?  For floor([1, 3/2]) = 1, which IS continuous in the calculus epsilon-delta sense.

Or am I missing something?

George

On Jul 2, 2011, at 9:07 AM, Kreinovich, Vladik wrote:

> Of course, the notion of contnuity depends on topology, but when people talk about continuity without explaining what this means, they mean continuity in the normal calculus epsilon-delta sense in which the floor function is clearly NOT continuous.
>
> ________________________________________
> From: stds-1788@xxxxxxxx [stds-1788@xxxxxxxx] On Behalf Of Nate Hayes [nh@xxxxxxxxxxxxxxxxx]
> Sent: Friday, July 01, 2011 3:37 PM
> To: Jürgen Wolff von Gudenberg
> Cc: John Pryce; Dominique Lohez; stds-1788@xxxxxxxx
> Subject: Re: KISS-decorations
>
> I'm thinking along the lines of Definition 2.2.3 on pp. 55-56 in:
>    http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF
> By that definition, wouldn't
>    floor([1,3/2])
> be continuous?
>
> Nate
>
>
> ----- Original Message -----
> From: "Jürgen Wolff von Gudenberg" <wolff@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
> To: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
> Cc: "John Pryce" <j.d.pryce@xxxxxxxxxxxx>; "Dominique Lohez"
> <dominique.lohez@xxxxxxx>; "stds-1788@xxxxxxxx" <stds-1788@xxxxxxxx>
> Sent: Friday, July 01, 2011 2:59 PM
> Subject: Re: KISS-decorations
>
>
>> Nate
>>
>> Am 01.07.2011 17:09, schrieb Nate Hayes:
>>> One other comment:
>>>
>>> What about
>>> floor([1,3/2])?
>>> I would think it should be defined and continuous, i.e., "safe", since
>>> when
>>> restricted to the domain [1,3/2] the floor function at 1 is defined and
>>> continuous when approached from the right and cannot be approached from
>>> the
>>> left.
>>>
>>> But it seems this would imply
>>> floor([1,1])
>>> should also be "safe"; but motion 27 gives "defined" for this example?
>>>
>>> Nate
>>>
>> I think 1 is a discontinuity point of the floor function, hence both cases
>> are defined only
>> Juergen
>>

Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave
Milwaukee WI 53201-1881 USA
414-288-6599; GasDay: 288-4400; Fax 288-5579
George.Corliss@xxxxxxxxxxxxx
www.eng.mu.edu/corlissg