SPEAKER: Jeff Norden

TITLE: *
Fun with Fixed Points
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Given a function *f* from a set to itself, a **fixed point** of *f* is just what you should expect: a point that doesn't move. To be more precise, it is a point *x* such that *f(x)=x*

Fixed points occur in many different settings. I'll discuss some of the ones that I find interesting.

Here is an easy but fun problem that you can certainly work out yourself. Let
*X* be a **finite** set and let *f* be a function from *X* to itself which is chosen
randomly from all such functions. Show that the probability that *f* has at
least one fixed point is more than 63.2% (i.e., 79 out of 125).

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