From cd8b8c25ea0a23ef2ef148a8504913aef8428ac1 Mon Sep 17 00:00:00 2001 From: jim Date: Fri, 20 Feb 2015 13:51:31 -0500 Subject: [PATCH] revised inf arithmetic question again, like to ordinals, cardinals --- exercises/_assignment4.mdwn | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) 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 ξ <~~> ξ`. 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 ξ 1 <~~> ξ`, where `ξ` is the fixed point you found in (1). What about `add ξ 2 <~~> ξ`? -- 2.11.0