X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=exercises%2F_assignment4.mdwn;h=f998e7ac73a33c66d353463a62b91aa7b403d710;hp=226741e14c1f136f738019543eeea238351aa9fa;hb=ea4c96609b8d02f5e83a8027cf567bab5562cb5b;hpb=f18d270f9c73466e1ec28afb184a0fdb3fc343af diff --git a/exercises/_assignment4.mdwn b/exercises/_assignment4.mdwn index 226741e1..f998e7ac 100644 --- a/exercises/_assignment4.mdwn +++ b/exercises/_assignment4.mdwn @@ -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 [[!wiki ordinal numers]], 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 `+` and `*` are defined in such a way that `inf + n` is different from `n + inf`, and does exceed `inf`.) 9. Prove that `add Î¾ 1 <~~> Î¾`, where `Î¾` is the fixed point you found in (1). What about `add Î¾ 2 <~~> Î¾`? @@ -117,8 +117,8 @@ 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)` (recall this is shorthand for `\x. add x n`) may not be a fixed point for `(*n)` or for +`(^n)`. ## Mutually-recursive functions ##