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Back in the old days, I had a book that listed many things about math tables and symbols. What is the modern equivalent book?

My question was unclear. I think it was because I used one question in the title and another in the body of the post. Leave it closed.

  • Welcome to Mathematics Stack Exchange. $\mapsto$ produces $\mapsto$, as in $f:\mathbb R\to\mathbb R$ defined by $f:x\mapsto x^3$ – J. W. Tanner Mar 10 '20 at 02:35
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    @J.W.Tanner as far as I am aware, the arrow $\to$ is for the mapping between domain and codomain, where as the arrow $\mapsto$ is for the mapping between input and output. – Mr Pie Mar 10 '20 at 02:41
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    @MrPie: isn't that consistent with my example? – J. W. Tanner Mar 10 '20 at 02:46
  • In the function notation, like $f:A\mapsto B$, I know it to represent an injective mapping. This is how my professor taught and Ive seen it in multiple books and a couple of papers, though I dont personally use the notation. – CogitoErgoCogitoSum Mar 10 '20 at 02:48
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    @CogitoErgoCogitoSum: isn't that $\Large\hookrightarrow$? cf. this question – J. W. Tanner Mar 10 '20 at 02:57
  • I edited the question to make it clear that I was asking for a modern equivalent book, not the modern equivalent of the symbol. –  Mar 10 '20 at 03:04
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    @J.W.Tanner -- My guess is he might be thinking of $↣$, which I recall being used in my category theory class a lot to represent monomorphisms (which are injections in the category of sets). Though looking it up here, it appears that symbol has other uses, maybe? I'm not versed enough in category theory to properly say for sure though. Just a thought (and sorry for assuming if I'm wrong, CogitoErgoCogitoSum). – PrincessEev Mar 10 '20 at 03:05
  • @GeoGraphy: in "modern" times, you can look up symbols on line (e.g., detexify), rather than in a book – J. W. Tanner Mar 10 '20 at 03:09
  • @J.W.Tanner I didn't see the last part of your comment, sorry :P – Mr Pie Mar 10 '20 at 09:04

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This symbol has no "modern equivalent," to my understanding, because it is still in use today.

$x \mapsto y$ means, for an implied function $f$, that $f$ maps $x$ to $y$, i.e. $f(x)=y$. You might have each side of the arrow written in a general form, such as $x \mapsto x^2$ denoting $f(x)=x^2$, or to denote a particular mapping of elements, such as $2 \mapsto 4$ as under the previous example.

PrincessEev
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  • Perhaps I should have asked the difference tween the symbol ↦ and the symbol →. –  Mar 10 '20 at 03:10
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    $\to$ usually is used in the definition of the function itself. $f : A \to B$ would be such an example case, where this usage means $A$ is the domain of the function $f$, and $B$ is the codomain of the function. So in that sense, the difference is -- $\mapsto$ is usually used to specify the definition of the mapping itself (i.e. how are elements mapped to each other), while $\to$ is more concerned with the general definition (i.e. which sets are mapped into each other). – PrincessEev Mar 10 '20 at 03:13