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Theorem: Suppose $n \in \mathbb N$ and for each $i \in \mathbb N, (X_i, \tau_i)$ is a metric space . All conserving metrics on $\Pi_{i=1} ^{n}X_i$ are lipschitz equivalent. In particular, each is lipschitz equivalent to the euclidean product metric $\mu_2$ on $\Pi_{i=1} ^{n} X_i$
Proof. Suppo...
In the study of metric spaces in mathematics, there are various notions of two metrics on the same underlying space being "the same", or equivalent.
In the following,
X
{\displaystyle X}
will denote a non-empty set and
d
1
{\displaystyle d_{1}}
and
d
2
{\displaystyle d_{2}}
will denote two metrics on
X
{\displaystyle X}
...
I've noticed we have both legendre-symbol and quadratic-residues. Would it make sense to make the former an alias of the latter?
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