The Time Hierarchy Theorem establishes separation only up to a constant factor overhead, and Blum's speedup theorem shows some functions resist any fixed complexity classification.

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Blum's speedup theorem(as used in computational complexity theory): A mathematical discovery by computer scientist Manuel Blum showing that some computational problems can always be solved faster, no matter what method you're currently using.
Complexity classification(as used in computer science): A way of sorting computational problems into categories based on how hard they are to solve or how many resources they require.
Constant factor overhead(as used in computational complexity): A fixed amount of extra effort or resources needed; for example, if task B always takes exactly 3 times as long as task A, that '3 times' is the constant factor.
Manuel Blum(as a historical figure in computer science): A pioneering computer scientist known for his work on computational complexity—the study of how difficult different problems are for computers to solve.

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