From: jim Date: Fri, 20 Feb 2015 18:51:31 +0000 (-0500) Subject: revised inf arithmetic question again, like to ordinals, cardinals X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=cd8b8c25ea0a23ef2ef148a8504913aef8428ac1 revised inf arithmetic question again, like to ordinals, cardinals --- diff --git a/exercises/_assignment4.mdwn b/exercises/_assignment4.mdwn index f998e7ac..127ecc39 100644 --- a/exercises/_assignment4.mdwn +++ b/exercises/_assignment4.mdwn @@ -99,7 +99,7 @@ point, i.e., demonstrate that `succ Î¾ <~~> Î¾`. We've had surprising success embedding normal arithmetic in the Lambda Calculus, modeling the natural numbers, addition, multiplication, and so on. But one thing that some versions of arithmetic supply is a -notion of infinity, which we'll write as `inf`. This object usually +notion of infinity, which we'll write as `inf`. This object sometimes satisfies the following constraints, for any finite natural number `n`: n + inf == inf @@ -107,7 +107,7 @@ satisfies the following constraints, for any finite natural number `n`: n ^ inf == inf leq n inf == true - (Note, though, that with *some* notions of infinite numbers, like [[!wikipedia ordinal numbers]], operations like `+` and `*` are defined in such a way that `inf + n` is different from `n + inf`, and does exceed `inf`.) + (Note, though, that with *some* notions of infinite numbers, like [[!wikipedia ordinal numbers]], operations like `+` are defined in such a way that `inf + n` is different from `n + inf`, and does exceed `inf`; similarly for `*` and `^`. With other notions of infinite numbers, like the [[!wikipedia cardinal numbers]], even less familiar arithmetic operations are employed.) 9. Prove that `add Î¾ 1 <~~> Î¾`, where `Î¾` is the fixed point you found in (1). What about `add Î¾ 2 <~~> Î¾`?