[taos-glug] Re: Courant & Robbins; I'm also enjoying Chapter 2, atleast . . .
- From: Jonathan Bartlett <johnnyb@xxxxxxxxxx>
- To: taos-glug@xxxxxxxxxxxxx
- Date: Thu, 14 Aug 2003 15:13:57 -0700 (PDT)
> . . . so far. But I skipped the entire section on interval arithmetic
> and especially Ex. 2.16, in view of the authors' warning).
It ends up it's harder than I thought. My plan was to break it up into a
"centerpoint" and "tolerance" value (expressed as a percentage) and a
list consisting of the entire history of intervals used to make this one.
When performing an operation, the tolerance would only be manipulated if
you are introducing a new interval which had not participated in that
history. The problem is that addition and multiplication modify
tolerances in different ways, and I'm not sure how to account for that.
Jon
> I enjoyed, by the way, Exercise 2.5, where you have to represent pairs
> as integers.
>
> It reminded me of an interesting chapter in a book called "What Is
> Mathematics?"
> by Courant and Robbins.
>
> In that book, there is a description of Cantor's proofs of the
> "denumerability" on the
> "rational" numbers, and the "non-denumerability" of the "real" numbers.
>
> Some of the other chapters of that book also seem to me to related to topics
> in SICP, for example the "continued fractions" of Exercise 1.37.
>
>
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