Of course I said, "It's still infinity! What's the best way to think about the infinite ordinals. "Anything divided by itself equals one"** wrote on Feb 03, 2007: I once thought up of a way of doing the Grand Hotel in Haskell, by using an infinite list: First off, your implementation of infinity is probably among the saner possible with a Peano arithmetic. You'd have to ask somebody who knows more math than I do (or check Wikipedia). Especially the one-point compactification of R (or ... well ... machine-R) you'll find as As always with “infinity” you should apply Bustany's Rule of Infinity: > Infinity and Intuition do not mix So chuck out your intuition and ask: > Which infinity? 2/20000000000= 1/10000000000 which is very close to 0. Note that there is a lot of theory going on 'behind the scenes' so to speak that we are not going to cover in this section. Any number divided by infinity is equal to 0. Why don't libraries smell like bookstores? Eric Kidd Alan Manuel Gloria Think of dividing 2 by a very big number. It is 0. 2. And as I work through various sections, I'm increasingly convinced that my understanding of some of the ideas is still pretty dodgy. This is also true for 1/x 2 etc : A function such as x will approach infinity, as well as 2x, or x/9 and so on. Sometime back in elementary school, I first asked teachers, "What happens when you divide infinity by 2?" We can write that in Haskell as: Math geeks in the audience will recognize this as the Peano arithmetic. data CompleteNumbers = Number Numbertype | Infinity Any expression divided by infinity is equal to zero. bigger and bigger, the Now, to answer our original question, what do we get when we divide infinity by 2? Jim Apple This equation is obvious incorrect. **Response to below: Inifinty divided by infinity would equal one. At least for the infinity Aleph-0. $\begingroup$ Related: What is infinity divided by infinity? 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. 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 . Or if you're looking for something else to read, here's a list of popular posts. We need to replace each Succ with Succ (Succ ...), which we can do with a recursive function: Dividing is trickier still, because we're working with natural numbers, which means we'll need to round down. 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 . Hard to wrap your mind around, but it's true. How long will the footprints on the moon last? Some professor wrote about something called transreal arithmetic. Therefore, infinity divided by infinity is NOT equal to one. What is the conflict of the story of sinigang? Who of the proclaimers was married to a little person? Infinity + Infinity = Infinity You could claim 2 X Infinity is the answer, that just equals Infinity. Summary: I think we should represent countable ordinals as the limits of increasing functions from the naturals to the countable ordinals. When did organ music become associated with baseball? ", More recently, a couple of friends were discussing a similar question at lunch: "What happens when you add 1 to infinity?". Random code snippets, projects and musings about software from Eric Kidd, a developer and entrepreneur. 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… What is plot of the story Sinigang by Marby Villaceran? wrote on Feb 08, 2007: A caution: I'm still studying the paper by Fokkinga and Meijer. $\endgroup$ – user2314737 Aug 27 at 10:24 add a comment | 2 Answers 2 Want to contact me about this article? or as Some teachers couldn't answer, and others told me, "It's still infinity! Inter state form of sales tax income tax? Using this definition of Nat, we can now define some numbers: OK, I threw in that last example just for fun. when you have a formal infinity, 1/infinity becomes an infinitesimal number, so you can develop non-standard analysis. You're welcome to. Is evaporated milk the same thing as condensed milk? That value is indeterminate, because infinity divided by infinity is defined as indeterminate, and 2 times infinity is still infinity. You can find a review in the Journal of Logic, Language and Information. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. = 1. All Rights Reserved. I'm not saying … Also, if you liked this article, you might want to check out The Haskell Road to Logic, Maths and Programming, which uses Haskell to teach discrete math. wrote on Feb 03, 2007: I posted my reply at http://japple.blogspot.com/2007/02/countable-ordinals-in-haskell.html Doubling a number is a bit trickier. Is it possible to represent any other (more interesting and/or more correct) definitions of infinity in Haskell?


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