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Can anyone explain what the phrase means? To be specific, my notes has the phrase "let $f:A \rightarrow B $ be the inclusion". Does this mean the identity map?

Michael Hardy
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jh4
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  • According to one fastidious usage, "$x$ contains $y$" means $y\in x$ but "$x$ includes $y$" means $y\subset x$. That makes sense because people say "partially ordered by inclusion" but never (as far as I know, but what do I know?) "partially ordered by containment". But that fastidious usage fails to be universally or even very widely adhered to by mathematicians, except in some contexts like that of your question or the "partially ordered" locution. At any rate, they're saying $B$ includes $A$, i.e. $A\subseteq B$, and $f(a)=a$ for $a\in A$. ${}\qquad{}$ – Michael Hardy Jan 08 '15 at 17:10
  • https://www.goodreads.com/quotes/24499-be-the-change-that-you-wish-to-see-in-the – Will Jagy Jan 08 '15 at 19:44

1 Answers1

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It means that $A\subseteq B$ and that $f(a)=a$ for every $a$ in $A$. But $f$ is not the identity map unless $B=A$.

Did
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