The Limit As A (Partial) Function

In math, we often say the limit of a function. This is not precise. A better phase is “the limit of a function at a point” since limits are always defined with respect to a function and a point.

Say we have a function and we want to find the limit at the point . We can write as to emphasize that the limit is a binary function, with the following type signature (in Haskell):

lim :: (a -> b) -> a -> b

Except that it’s not quite a function. The limit does not always exist at a point. So perhaps a better type signature is

lim :: (a -> b) -> a -> Maybe b

Related Posts

How I feel about ebooks

List of places where the US has been involved in regime change, with multiplicity

Accuracy vs Precision

Handy command line benchmarking tool

Stan Rogers

Ultimate Hot Couch Guy

Quote on Java Generics

The Programmer Tendency

Figure out undocumented JSON with gron

Mental Model of Dental Hygiene