Why your intuition about growth rates might be slightly off
In short: When functions head toward infinity, they don't all travel at the same speed. This video breaks down the mathematical hierarchy of growth, proving why some common functions eventually dwarf others.
The video establishes a clear order of operations for asymptotic growth as $n$ becomes large. While exponentials are often perceived as the pinnacle of speed, they are actually surpassed by factorials and $n^n$.
The hierarchy moves from the slowest to the fastest: logarithms are the slowest, followed by polynomials (like quadratics), then exponentials, then factorials, and finally $n^n$. The presentation uses the big theorem for limits to prove these relationships mathematically.
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Sources
- Summary by Intellect · source: The Hierarchy of Big Functions || n^n greater than n! greater than e^n greater than n^100
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