What's a real world example of double exponential function and factorial function?

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As the title asks. I'm looking to create very fast growing numbers.

If there's a better solution than these two please let me know as well.

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Factorial is the number of ways to shuffle a deck of $n$ cards. Double exponential function appears in the Gompertz-Makeham law of mortality. But you don't have to search the real world in order to create very fast growing numbers. Quite the opposite, in fact. Numbers do not exist in the real world.

If you want something that grows really fast, you may take a look at the Ackermann function.