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Merge pull request #12 from walkingsophie/patch-1
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zeramorphic authored Sep 21, 2023
2 parents 0481fe9 + ae87e95 commit d8d883a
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2 changes: 1 addition & 1 deletion ib/antop/03_metric_spaces.tex
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Expand Up @@ -3,7 +3,7 @@ \subsection{Definition}
Let \( M \) be a set.
Then a \textit{metric} on \( M \) is a function \( d \colon M \times M \to \mathbb R \) such that
\begin{enumerate}
\item (positivity) \( \forall x,y \in M, d(x,y) \geq 0 \), and in particular, \( x = y \iff d(x,x) = 0 \)
\item (positivity) \( \forall x,y \in M, d(x,y) \geq 0 \), and in particular, \( x = y \iff d(x,y) = 0 \)
\item (symmetric) \( \forall x,y \in M, d(x,y) = d(y,x) \)
\item (triangle inequality) \( \forall x,y,z \in M, d(x,z) \leq d(x,y) + d(y,z) \).
\end{enumerate}
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