High school
A function gives one output for each permitted input.
A machine that squares its input sends 2 to 4 and −2 to 4. Different inputs may share an output. A single input must not give two different answers.
Think with the concrete example above. You can try again.
The squaring machine does exactly this. A function forbids two different outputs for the same input, not one shared output for two inputs.
Your answer fits this explanation. Look for the same idea in the comic.
Yes; each input still has one output. The squaring machine does exactly this. A function forbids two different outputs for the same input, not one shared output for two inputs.
A rule that sends x to x × x sends both 2 and −2 to 4. It is still a function.
FLT · aa2d8b3 · Def_FLTPrelim_Modularity.lean
def qCoeff (f : ℍ → ℂ) (n : ℕ) : ℂ :=(qExpansion 1 f).coeff n
The input f is itself a function. ℍ → ℂ says its input is a point of the upper half-plane and its output a complex number. The additional n selects a coefficient.
Functions
Read the three explanation steps first. The Lean source is there for a closer look afterwards; you do not have to read it first.
A function gives one output for each permitted input.
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A rule that sends x to x × x sends both 2 and −2 to 4. It is still a function.
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