# Revisiting Fixed Point: What does it mean in the world of computer science?

A while ago I asked Fixed point, what does it mean in the world of computer science?

While the answers did help me to understand what Fixed point meant, the answers left me in a murky world when ever I thought about what a fixed point meant. In other words, no clear definition poped into my mind and I would wonder about in thought trying to match up a definition with what I was trying to learn or understand.

Today I was watching the video Categories for the Working Programmer by Jeremy Gibbons in which he stated: (Time index: 33:00)

It's fix point because it's the solution of a recursive equation.

And I thought that makes sense; is it really that simple?

So the question is:

Can the definition of fix point be thought of simply as

"It's the solution of a recursive equation."

A fixed point of a function $f$ is an element $x$ satisfying $f(x) = x$. A solution to a recursive equation can be put in that form.

• Thanks. I will take it that the comment in the video is too simple and rely on the definition you reiterated here as the first one to use when thinking about fixed point. – Guy Coder Feb 12 '16 at 15:37