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wingsoflight

  • one year ago

Use a proof by cases to show that min(a , min(b, c» = min(min(a , b) , c) whenever a, b, and c are real numbers.

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  1. satellite73
    • one year ago
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    i guess you can grind it out with cases, for example if \(a\leq b\leq c\) then \[\min(a, (\min(b,c))=\min(a, b)=a\]

  2. satellite73
    • one year ago
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    similarly if \(a\leq c\leq b\) then \(\min(a,\min(b,c))=\min(a,c)=a\) and so on

  3. wingsoflight
    • one year ago
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    thank you for clear answer

  4. satellite73
    • one year ago
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    oh i guess you have to say for the first one that \(\min(a, \min(b,c))=a=\min(\min(a,b),c)\)

  5. satellite73
    • one year ago
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    likewise for the second. there may be a snappier way to do this, but it did say by cases, so just grind it out

  6. satellite73
    • one year ago
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    yw

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