[Question] What Are The Preconditions/​Prerequisites for Asymptotic Analysis?

Under what conditions is describing the behaviour of a (physical or abstract) process using asymptotic apparatus sensible/​productive/​reasonable?

Kinds of replies that I would find especially valuable:

  • Formal properties that a function (or collection thereof) must satisfy for applying asymptotic analysis to be sensible

  • Heuristics for when applying asymptotic analysis to real world processes is productive

  • Examples of real world processes satisfying the above

  • Examples of processes/​functions that might seem amenable to asymptotic analysis but which it would actually be a mistake to try and consider through an asymptotic lens

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