Re: new article, "A Romp Through Infinity"

On Thu, Aug 7, 2008 at 11:31 AM, Will Coleda <[EMAIL PROTECTED]> wrote: > On Thu, Aug 7, 2008 at 11:29 AM, <[EMAIL PROTECTED]> wrote: >> Supporting multiple levels of infinities, transfinite numbers or even >> Surreal Numbers should be considered in the same category of features as >> returning

Re: new article, "A Romp Through Infinity"

On Thu, Aug 7, 2008 at 11:29 AM, <[EMAIL PROTECTED]> wrote: > Supporting multiple levels of infinities, transfinite numbers or even Surreal > Numbers should be considered in the same category of features as returning > multiple answers from complex trig functions. > > They're an interesting thin

Re: new article, "A Romp Through Infinity"

TSa Thomas.Sandlass-at-barco.com |Perl 6| wrote: HaloO, [EMAIL PROTECTED] wrote: Let's just make sure we're handling inf and -inf right and leave all that other stuff until later. The point is: what is the minimum we need to be future proof and compatible to other language features. Regards

Re: new article, "A Romp Through Infinity"

TSa Thomas.Sandlass-at-barco.com |Perl 6| wrote: Could we get confirmation for that from @Larry. I remember $Larry mentioning that Num fails over to Rat or so when necessary. IOW, does my Rat $rat = 1/3; # assuming infix: returns a Rat my Num $num = 1/3; my Rat $diff = abs($rat - $n

Re: new article, "A Romp Through Infinity"

Xavier Noria fxn-at-hashref.com |Perl 6| wrote: IMO to include something related to infinity you need to stick with some particular model and forget the rest. I couldn't have said it any better.

Re: new article, "A Romp Through Infinity"

HaloO, [EMAIL PROTECTED] wrote: Let's just make sure we're handling inf and -inf right and leave all that other stuff until later. The point is: what is the minimum we need to be future proof and compatible to other language features. Regards, TSa. -- "The unavoidable price of reliability i

Re: new article, "A Romp Through Infinity"

HaloO, Xavier Noria wrote: IMO to include something related to infinity you need to stick with some particular model and forget the rest. Well spoken. But I think that the model John has chosen is a bit too restrictive. If a type has a notion of Zero it could have a similar notion of infinity

Re: new article, "A Romp Through Infinity"

Supporting multiple levels of infinities, transfinite numbers or even Surreal Numbers should be considered in the same category of features as returning multiple answers from complex trig functions. They're an interesting thing to discuss and experiment with but shouldn't distract form getting

Re: new article, "A Romp Through Infinity"

HaloO, John M. Dlugosz wrote: The proposed Infinite class (see the thread I started on 4/25/2008) does handle transfinite cardinals. Do you mean the thread called "The Inf type" where I replied to your post of a version of your specdoc? My concern with the approach you take there is to base it

Re: new article, "A Romp Through Infinity"

On Thu, Aug 7, 2008 at 3:19 PM, John M. Dlugosz <[EMAIL PROTECTED]> wrote: > I'm not sure. A quick reading indicates that ⋆ℝ contains "infinitely large" > numbers that maintain the properties of addition, but that is not the same > as "infinity". Well *R is a field that has infinitely large and

Re: new article, "A Romp Through Infinity"

TSa Thomas.Sandlass-at-barco.com |Perl 6| wrote: As I recall, it can handle the concept of Inf-1 etc. Yes. But the Hyperreals do the same and stay within the realm of set theory. I'm not sure. A quick reading indicates that ⋆ℝ contains "infinitely large" numbers that maintain the properti

Re: new article, "A Romp Through Infinity"

TSa Thomas.Sandlass-at-barco.com |Perl 6| wrote: Firstly, shouldn't there also be infinite strings? E.g. 'ab' x Inf is a regularly infinite string and ~pi as well. Other classes might have elaborate notions of infinity. A string whose length is Inf is not itself equal to Inf. But $s.chars > $b

Re: new article, "A Romp Through Infinity"

HaloO, I wrote: That is you can do the usual Int arithmetic in the ranges Inf..^Inf*2 and -Inf*2^..-Inf except that Inf has no predecessor and -Inf no successor. Well, and we lose commutativity of + and *. I.e. 1 + $a != $a + 1 if $a is transfinite. Well, we can of course count downwards from

Re: new article, "A Romp Through Infinity"

HaloO, John M. Dlugosz wrote: Please let me know if you see any coding errors, and of course any feedback is welcome. Firstly, shouldn't there also be infinite strings? E.g. 'ab' x Inf is a regularly infinite string and ~pi as well. Other classes might have elaborate notions of infinity. The C

new article, "A Romp Through Infinity"

This weekend I wrote which explains the Inf features of Perl 6, but drills down each example to reach the most fundamental language features, which it explains. It should be interesting to those just taking the plunge to Perl 6 because so m