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What is the meaning of $\lor$ and $\land$ in the following function:$$\phi(x):= (x\land1)\lor(-1)$$ To give a little context, this should be a bounded transformation to bound a correlation estimator to $-1$ and $1$. I know of their use in logic but I've never seen them used like this.

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  • $\begingroup$ these should be max and min (I’ve often seen those notation in stats : $x∧y$ is $min(x,y)$), so the result is to bound the expression to 1 and -1 as you said $\endgroup$ – Nephanth May 2 at 17:43
  • $\begingroup$ Also: math.stackexchange.com/q/610760/42969: “$\wedge$ denotes min, while $\vee$ denotes max.” $\endgroup$ – Martin R May 2 at 17:46
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If you represent false and true as $0$ and $1$ respectively, $x\land y=\min\{x,\,y\}$ while $x\lor y=\max\{x,\,y\}$ (verify these with a truth table if you like). This $\land=\min,\,\lor=\max$ identification is the basis of semilattices. Using it on real numbers is just a very boring example of a lattice (i.e. a semilattice with both, satisfying absorption laws).

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