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 \(f\) and we want to find the limit at the point \(p\). We can write \(lim_{x \to p} f(x)\) as \(l(f,p)\) 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

Random Thought: LC Theorem

I finally have an answer to "who's your favorite singer?"

My Top Tip for Helping People Get Started Programming

GPT-f

Random paper on angles

An Image is Worth 16x16 Words

Random stuff

Lossless Data Compression with Neural Networks by Fabrice Bellard

Downscaling Numerical Weather Models With GANs (My CI 2019 Paper)

Learning Differential Forms and Questions