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I don't understand the algebra used in the below example proof from my textbook. Where does the + 1 come from? Is it okay to just add 1 anywhere you want? Or is there some rule here or reason you can?

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    $\begingroup$ $2r - 2s - 1 = 2r - 2s - 2 + 1 = 2(r - s - 1) + 1$ $\endgroup$ – Artem Mavrin Apr 25 '16 at 4:16
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$$2r-2s-1=2r-2s-1-1+1=2r-2s-2+1=2(r-s-1)+1$$

You can subtract 1 and plus 1 to balance things up. Something like adding zero, hence you preserve the equality.

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  • $\begingroup$ Ahhh...that makes complete sense! Thanks for your example! $\endgroup$ – timbram Apr 25 '16 at 4:21

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