Take a certain positive number and square it to get a distinct number, then square it again to get yet another distinct number, and then again, and so on indefinitely.
If the limiting value converges to a finite number what is
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Relevant wiki: Nested Functions
Pick a positive number.
If the number you pick is greater than 1, than it will become bigger at an increasing rate.
If the number you pick is equal to 1, it will stay at 1, not giving distinct numbers.
If the number you pick is less than 1, it will continually get smaller, but by a smaller amount. For example, if you pick 1/2:
1/2 -> 1/4 -> 1/16 -> 1/256...
It is easy to see that it converges at 0.