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TIFR2021-Maths-B: 6

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Define a metric on the set of finite subsets of $\mathbb{Z}$ as ollows:

$$d(A,B)=\text{the cardinality of } (A\cup B \backslash (A\cap B)).$$

The resulting metric space admits an isometry into $\mathbb{R}^n,$ for some positive integer $n$.
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