X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=exercises%2F_assignment4.mdwn;h=38e3180f6f8d79c83e9d965496023f53041aaedb;hp=33c7e779c648643843d734ea71696bb54252c593;hb=701998a14b92fc759963d258f2e425587a246d48;hpb=5c234a526ad9ecc96ae9d17b6f74de53a0354444 diff --git a/exercises/_assignment4.mdwn b/exercises/_assignment4.mdwn index 33c7e779..38e3180f 100644 --- a/exercises/_assignment4.mdwn +++ b/exercises/_assignment4.mdwn @@ -107,18 +107,18 @@ 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, 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 [[!wiki ordinal numers]], operations like `+` and `*` are defined in such a way that `inf + n` is different from `n + inf`, and does exceed `inf`.) -9. Prove that `add 1 Î¾ <~~> Î¾`, where `Î¾` is the fixed -point you found in (1). What about `add 2 Î¾ <~~> Î¾`? +9. Prove that `add Î¾ 1 <~~> Î¾`, where `Î¾` is the fixed +point you found in (1). What about `add Î¾ 2 <~~> Î¾`? Comment: a fixed point for the successor function is an object such that it is unchanged after adding 1 to it. It makes a certain amount of sense to use this object to model arithmetic infinity. For instance, depending on implementation details, it might happen that `leq n Î¾` is true for all (finite) natural numbers `n`. However, the fixed point -you found for `succ` may not be a fixed point for `mult n` or for -`exp n`. +you found for `succ` and `(+n)` may not be a fixed point for `(*n)` or for +`(^n)`. ## Mutually-recursive functions ##