We have $ (f \circ g) = x \mapsto f(g(x)) $ however since I read left to write it always seems backwards to me. Is there a symbol like $ ( g \ggg f) = x \mapsto f(g(x)) $.

It is especially grating in situations like.

$$ \require{AMScd} \begin{CD} X @>{f \circ g}>> Y \\ @VVgV @AAfA \\ g(X) @>{id}>> g(X)\end{CD} $$

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    $\begingroup$ I've seen people denote $g(f(x))$ by $(f\circ g)(x)$ in the context of group theory. $\endgroup$ – Git Gud Oct 23 '16 at 23:16
  • $\begingroup$ That's unpleasantly ambitious :( $\endgroup$ – Q the Platypus Oct 23 '16 at 23:19
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    $\begingroup$ I think the idea is that $f$ and $g$ appear in the same order in both notations. That's what we get for having left-hand function notation. Were I to go back in time to the ancient Greeks and reboot mathematics, I would establish the notation $(x)f$ (or maybe use something different from parentheses). Along with establishing $6.28$ as the circle constant (I would probably still call it $\pi$, for "perimeter", though), and the electron as positively charged. $\endgroup$ – Arthur Oct 23 '16 at 23:19
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    $\begingroup$ @QthePlatypus Actually that's not what I've seen. Arthur's comment reminded me of it. What I've seen is $(x)(f\circ g)$ denoting $g(f(x))$. $\endgroup$ – Git Gud Oct 23 '16 at 23:49
  • $\begingroup$ If you write your functions on the right, $x \mapsto xf$, then $fg$ means first do $f$ then $g$. Too bad the convention of writing functions to the left of their arguments got started a long time ago. $\endgroup$ – user4894 Oct 24 '16 at 0:41

Computer scientists may write g ; f for f ∘ g

See:Function composition - Alternative notations


I personally use the notation $f$»$g$, which is inspired by the F# operator >>. Perhaps you like that too, although it isn't established by any means.

In LaTeX it should be \text{\guillemotright} with:




Some math books (especially abstract algebra) may write composition in the reverse order: $\sigma\tau$ means: first $\sigma$ then $\tau$. For notation they write $$ x^{\sigma \tau} = \big(x^\sigma\big)^\tau $$ For example, this may be seen with field automorphisms.


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