Usefulness of the "not in" operator

[Terry Reedy]

On 10/10/2011 1:55 PM, Ian Kelly wrote:
> On Mon, Oct 10, 2011 at 11:33 AM, Chris Angelico<rosuav at gmail.com>  wrote:
>> On Tue, Oct 11, 2011 at 4:29 AM, Nobody<nobody at nowhere.com>  wrote:
>>>
>>> The Church numeral for N is a function of two arguments which applies its
>>> first argument N times to its second, i.e. (f^N)(x) = f(f(...(f(x))...)).
>>>
>>
>> Thanks - nice clear explanation. Appreciated. For an encore, can you
>> give an example of where this is actually useful? It seems a pretty
>> narrow utility.
>
> It's useful for writing mathematical theorems about computability with
> regard to the natural numbers using lambda calculus.

Whereas pure set theorists define counts as sets so they can work with 
counts within the context of pure set theory (in which everything is a 
set). Other mathematicians use an axiomatic definition which pretty much 
abstracts the common features of the set and function definitions.

-- 
Terry Jan Reedy