(properties of mulitiplication of inequalities) |
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Is there a formal way of saying a<b and c<d implies ac<bd, like a theorem from algebra or something? Just wondering because I used it for my inductive step. | Is there a formal way of saying a<b and c<d implies ac<bd, like a theorem from algebra or something? Just wondering because I used it for my inductive step. | ||
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| + | I believe the way you wrote it should be fine for the proof. | ||
[[Category:MA375Spring2009Walther]] | [[Category:MA375Spring2009Walther]] | ||
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| + | [[Category:MA375Spring2009Walther|inequality multiplication]] | ||
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| + | There is a property of inequalities that states: <br/> | ||
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| + | if c is some positive number and a < b, then ac < bc <br/> | ||
| + | if c is some negative number and a < b, then ac > bc <br/> | ||
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| + | From this property we can prove inequalities such as the following: | ||
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| + | If a<b and c<d, where a, b, c, and d are positive numbers then ac<bd must be true. | ||
Latest revision as of 06:44, 29 January 2009
Is there a formal way of saying a<b and c<d implies ac<bd, like a theorem from algebra or something? Just wondering because I used it for my inductive step.
I believe the way you wrote it should be fine for the proof.
There is a property of inequalities that states:
if c is some positive number and a < b, then ac < bc
if c is some negative number and a < b, then ac > bc
From this property we can prove inequalities such as the following:
If a<b and c<d, where a, b, c, and d are positive numbers then ac<bd must be true.
