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2 Corrected function so the fixed points are as claimed.
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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
source | link

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.