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Maybe a stupid question but should we prove if a=b then (a+c)=(b+c) if we want to use this property? Can't find where it is given in the book. | Maybe a stupid question but should we prove if a=b then (a+c)=(b+c) if we want to use this property? Can't find where it is given in the book. | ||
| + | |||
| + | Dr. Alekseenko: Apparently, this equation a consequence of | ||
| + | |||
| + | <math> (a+c)-(b+c) = </math> | ||
| + | |||
| + | use associative law | ||
| + | |||
| + | <math> a + (c - b) + c =</math> | ||
| + | |||
| + | use commutative law | ||
| + | |||
| + | <math> a + (b + (-c)) + c =</math> | ||
| + | |||
| + | next associative law, again, | ||
| + | |||
| + | <math> a + b + ((-c) + c) =</math> | ||
| + | |||
| + | finally use axiom of zero, i.e., <math> (-c)+c =0 </math> we obtain | ||
| + | |||
| + | <math> a + b + 0 </math> | ||
| + | |||
| + | then, again by the zero axiom | ||
| + | |||
| + | <math> a + b </math> | ||
| + | |||
| + | Since we have just established it, you do not need to prove it in your homework. | ||
| + | (but you have to put a reference to this proof). | ||
| + | |||
| + | ---- | ||
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Maybe a stupid question but should we prove if a=b then (a+c)=(b+c) if we want to use this property? Can't find where it is given in the book.
Dr. Alekseenko: Apparently, this equation a consequence of
$ (a+c)-(b+c) = $
use associative law
$ a + (c - b) + c = $
use commutative law
$ a + (b + (-c)) + c = $
next associative law, again,
$ a + b + ((-c) + c) = $
finally use axiom of zero, i.e., $ (-c)+c =0 $ we obtain
$ a + b + 0 $
then, again by the zero axiom
$ a + b $
Since we have just established it, you do not need to prove it in your homework.
(but you have to put a reference to this proof).
