In this section we have a discussion on the types of infinity and how these affect certain limits. Why don't libraries smell like bookstores? And finally, some questions for mathematically sophisticated readers: Jerf mentions math education: I bet you could build a good number theory curriculum around that idea; giving number theory a REPL couldn't be all bad, given the abstraction of the topic. Want to contact me about this article? From what I understant it incorporates infinity and 1/0 as part of the numbering system. What is the birthday of carmelita divinagracia? ", More recently, a couple of friends were discussing a similar question at lunch: "What happens when you add 1 to infinity?". with the corresponding extensions to Ord and Num implemented specificially. Now, infinity is a subtle concept, and if had we used different definitions, we might have gotten a … How long does it take to cook a 23 pound turkey in an oven? If we type this into the listener, something entertaining happens: Haskell will happily keep printing this until we hit Control-C. And sure enough, add1 infinity is just another infinite list of Succ: We need to hit Control-C again. This section is intended only to give you a feel for what is going on here. Alan Manuel Gloria Infinity divided by two equals infinity. Any expression divided by infinity is equal to zero. ", but I couldn't explain it much better than my school teachers (at least not without using the word denumerable, which is a good way to ruin a lunch conversation). Properties of Infinity Addition with Infinity Infinity Plus a Number Infinity Plus Infinity Infinity Minus Infinity Multiplication with Infinity Infinity by a Number Infinity by Infinity Infinity by Zero Division with Infinity and Zero Zero over a Number A Number over Zero A Number over Infinity Infinity over a Number… or as (Why not use Haskell's built-in integers? So now you have (Infinity + Infinity) / Infinity = 1 ... 2013 by anonymous. Therefore, infinity divided by infinity is NOT equal to one. But other than that, it's pretty much the opposite of multiplying: How should we define infinity? How long will it take to cook a 12 pound turkey? I. Instead we can get any real number to equal to one when we assume infinity divided by infinity is equal to one, so infinity divided by infinity is undefined . $\endgroup$ – user2314737 Aug 27 at 10:24 add a comment | 2 Answers 2 At least for the infinity Aleph-0. Is it possible to represent any other (more interesting and/or more correct) definitions of infinity in Haskell? wrote on Feb 03, 2007: Eric Kidd Using this definition of Nat, we can now define some numbers: OK, I threw in that last example just for fun. Now, infinity is a subtle concept, and if had we used different definitions, we might have gotten a different result. The "deriving" keyword tells Haskell to define show and the comparison operators for us. Random code snippets, projects and musings about software from Eric Kidd, a developer and entrepreneur. Any number divided by infinity is equal to 0. Jim Apple You could also have done infinity as $\begingroup$ Related: What is infinity divided by infinity? What is plot of the story Sinigang by Marby Villaceran? You can find a review in the Journal of Logic, Language and Information. 2 + − 2 ∞ + 1 ∞ 2 + − 3 ∞ 3 1 + − 1 ∞ 2 + 1 ∞ 3 \frac {2+\frac {-2} {\infty }+\frac {1} {\infty ^ {2}}+\frac {-3} {\infty ^3}} {1+\frac {-1} {\infty ^ {2}}+\frac {1} {\infty ^3}} 1 + ∞ 2 − 1 + ∞ 3 1 2 + ∞ − 2 + ∞ 2 1 + ∞ 3 − 3 . bigger and bigger, the How will understanding of attitudes and predisposition enhance teaching? The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. you can also add a -Infinity, and it'll still be compatible with Peano axioms. wrote on Feb 03, 2007: I posted my reply at http://japple.blogspot.com/2007/02/countable-ordinals-in-haskell.html There's several ways we could do it, but one way is particularly natural in this framework. All Rights Reserved. Hard to wrap your mind around, but it's true. *Main> divBy2 infinity Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Well, that looks like infinity to me! 2/20000000000= Infinity + Infinity = Infinity You could claim 2 X Infinity is the answer, that just equals Infinity. We can write that in Haskell as: Math geeks in the audience will recognize this as the Peano arithmetic. First, we need to teach Haskell about the natural numbers. quotient approaches 0. And as I work through various sections, I'm increasingly convinced that my understanding of some of the ideas is still pretty dodgy. What is the conflict of the story of sinigang? You'd have to ask somebody who knows more math than I do (or check Wikipedia). 1/10000000000 which is very close to 0. Infinity is a concept, not an actual number, so we can't just divide a number by infinity. For example, http://spiedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PSISDG006499000001649902000001&idtype=cvips&gifs=yes, The Haskell Road to Logic, Maths and Programming, Smart classification using Bayesian monads in Haskell, Proving sorted lists correct using the Coq proof assistant, Lightweight Languages 2 Conference (MIT, 2002), Monads in 15 minutes: Backtracking and Maybe, Bare Metal Rust 3: Configure your PIC to handle interrupts correctly, Is it reasonable to define infinity this way, assuming we're in category. How long will the footprints on the moon last? What's the best way to think about the infinite ordinals. Some professor wrote about something called transreal arithmetic. Summary: I think we should represent countable ordinals as the limits of increasing functions from the naturals to the countable ordinals.
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