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ece108: add wlog

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eggy 2023-01-20 11:05:18 -05:00
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@ -256,6 +256,9 @@ $$n\text{ is a perfect square}\iff \exists k\in\mathbb Z,n=k^2$$
### Induction ### Induction
!!! definition
- A proof **without loss of generality** (WLOG) indicates that the roles of variables do not matter — so long as the symbols CTRL-H'd, the proof remains exactly the same. For example, "WLOG, let $x,y\in\mathbb Z$ st. $x<y$."
Induction is a proof technique that can be used if the open sentence $P(n)$ depends on the parameter $n\in\mathbb N$. Because induction works in discrete steps, it generally cannot be applied domains of all real numbers. Induction is a proof technique that can be used if the open sentence $P(n)$ depends on the parameter $n\in\mathbb N$. Because induction works in discrete steps, it generally cannot be applied domains of all real numbers.
To do so, the following must be proven: To do so, the following must be proven: