Use of "without loss of generality" - Mathematics Stack Exchange
https://math.stackexchange.com/questions/129137/use-of-without-loss-of-generality
WEBApr 7, 2012 · Without loss of generality, we can assume that $x=z+1$ for some $z \in \mathbb{Z}$. [In this case, $S=\mathbb{Z}$ and $T=\{z+1:z \in \mathbb{Z}\}$.] We want to show that $P(x)$ is true for all $x \in \mathbb{Z}$. Without loss of generality, we can assume that $x=5q+r$ where $q,r \in \mathbb{Z}$ and $0 \leq r < q$.
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