Re: Finding an upper Darboux integral

Noh wrote:

> Thanks so much for your help. Now I see.

Hopefully you also saw that not everything
I posted was completely correct. For example
(and this may not be the only example):

>> Finally, to show that
>>
>> upper D-integral of f on [0,b] \geq (b^2)/2,
>>
>> from which we then get
>>
>>
>> upper D-integral of f on [0,b] = (b^2)/2,
>>
>> note that right-endpoint Riemann sums of f
>> on [0,b] using equal length subintervals _are_
>> upper Darboux sums, and the supremum of all
>> these right-endpoint Riemann sums is (b^2)/2.
>> Hence, the supremum over all the upper Darboux
>> sums must be greater than or equal to (b^2)/2.

Each time I used the word "supremum", I should have
used "infimum".

A bad thunderstorm was arriving while I was proof
reading my post, so I hurriedly wrote a disclaimer
of sorts at the end of my post, sent my post in,
and then turned off and unplugged my computer.

(It's not often that I can point to a real excuse
when I get something wrong in here, and so I didn't
want to let this opportunity slip by!)

Dave L. Renfro

.