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From what I understand, these two notations are exactly the same. Can they be used interchangeably?

Ruochan Liu
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    Basically yes. But in my experience the second version is more often used for the general definition as opposed to a single value. That is, $f:x\mapsto x^2$ is more normal than $f:2\mapsto 4$. Not a hard rule though – Milten Oct 16 '21 at 18:06
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    I would only use the second formulation to indicate the general form of the function. Thus, with $f(x)=x^2$. I would write $f: x\mapsto x^2$ but I would not write $f:0\mapsto 0$, though of course $f(0)=0$. – lulu Oct 16 '21 at 18:07
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    Also note that $\mapsto$ allows you to talk about a function without giving it a name: $x\mapsto x^2$ is a function even without the name $f$. – Milten Oct 16 '21 at 18:07
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    The two notations are obviously not exactly the same. But they mean the same. – Dietrich Burde Oct 16 '21 at 18:12

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