Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

 2 Corrected function so the fixed points are as claimed. edited May 12 '15 at 12:46 David Richerby 75.9k1717 gold badges117117 silver badges208208 bronze badges A fixed point of a function $$f$$ is a value $$x$$ such that $$f(x)=x$$. A function might have no fixed points (e.g., $$f(x)=x+1$$), a finite number of them (e.g., $$f(x)=x^2-x-1$$$$f(x)=x^2+x-1$$) or infinitely many (e.g., $$f(x)=x$$ where $$x$$ comes from some infinite set). If $$x$$ comes from a set with an ordering relation, such as $$\leq$$ on some kind of numbers, or $$\subseteq$$ on sets and a function $$f$$ has at least one fixed point, it makes sense to talk about the least or greatest fixed point of $$f$$ with respect to that ordering. For example, on the real numbers, the fixed points of $$f(x)=x^2-x-1$$$$f(x)=x^2+x-1$$ are $$x=\pm 1$$: the greatest fixed point is $$+1$$ and the least fixed point is $$-1$$. I suspect the functions you're dealing with aren't functions on the real numbers but the same principles apply. A fixed point of a function $$f$$ is a value $$x$$ such that $$f(x)=x$$. A function might have no fixed points (e.g., $$f(x)=x+1$$), a finite number of them (e.g., $$f(x)=x^2-x-1$$) or infinitely many (e.g., $$f(x)=x$$ where $$x$$ comes from some infinite set). If $$x$$ comes from a set with an ordering relation, such as $$\leq$$ on some kind of numbers, or $$\subseteq$$ on sets and a function $$f$$ has at least one fixed point, it makes sense to talk about the least or greatest fixed point of $$f$$ with respect to that ordering. For example, on the real numbers, the fixed points of $$f(x)=x^2-x-1$$ are $$x=\pm 1$$: the greatest fixed point is $$+1$$ and the least fixed point is $$-1$$. I suspect the functions you're dealing with aren't functions on the real numbers but the same principles apply. A fixed point of a function $$f$$ is a value $$x$$ such that $$f(x)=x$$. A function might have no fixed points (e.g., $$f(x)=x+1$$), a finite number of them (e.g., $$f(x)=x^2+x-1$$) or infinitely many (e.g., $$f(x)=x$$ where $$x$$ comes from some infinite set). If $$x$$ comes from a set with an ordering relation, such as $$\leq$$ on some kind of numbers, or $$\subseteq$$ on sets and a function $$f$$ has at least one fixed point, it makes sense to talk about the least or greatest fixed point of $$f$$ with respect to that ordering. For example, on the real numbers, the fixed points of $$f(x)=x^2+x-1$$ are $$x=\pm 1$$: the greatest fixed point is $$+1$$ and the least fixed point is $$-1$$. I suspect the functions you're dealing with aren't functions on the real numbers but the same principles apply. 1 answered May 12 '15 at 10:40 David Richerby 75.9k1717 gold badges117117 silver badges208208 bronze badges A fixed point of a function $$f$$ is a value $$x$$ such that $$f(x)=x$$. A function might have no fixed points (e.g., $$f(x)=x+1$$), a finite number of them (e.g., $$f(x)=x^2-x-1$$) or infinitely many (e.g., $$f(x)=x$$ where $$x$$ comes from some infinite set). If $$x$$ comes from a set with an ordering relation, such as $$\leq$$ on some kind of numbers, or $$\subseteq$$ on sets and a function $$f$$ has at least one fixed point, it makes sense to talk about the least or greatest fixed point of $$f$$ with respect to that ordering. For example, on the real numbers, the fixed points of $$f(x)=x^2-x-1$$ are $$x=\pm 1$$: the greatest fixed point is $$+1$$ and the least fixed point is $$-1$$. I suspect the functions you're dealing with aren't functions on the real numbers but the same principles apply.