Show that {x} = x - [x] has period 1. Then find the period of {5x}.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Show that has period . Then find the period of .
Need a reminder? The key ideaShow
means . is the greatest integer not above , and lies in . A piecewise function uses the rule for the piece that holds the input.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Period . .
Step 2. . It repeats when grows by , that is when grows by .
Answer: has period , and has period .
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