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Thought is a non-example of density (unless you happen to be thinking about density!) Any abstract concept should fit the bill.
It is used to prove some of the statements used in Einstein's The general Theory of relativity
Functions must have a property of predictability. So, there will never be a function (hence then this is a non-function) to predict the nth digit of pi. We can calculate the digits of pi in order one at a time, but there will never be a function that will take us directly to the 1,001st digit of pi.
A non-repetitive pattern.