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nike5
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Homework Statement
The maximum of 2 numbers x and y is denoted by max(x,y) and the minimum of 2 numbers
x and y is denoted by min(x,y). Prove that max(x,y) = (x + y + l y - x l) / 2
and min(x,y) = (x + y - ly - xl ) / 2.
Homework Equations
The Attempt at a Solution
Theorem. max(x,y) = (x + y + l y - x l) / 2
Proof. Let x and y be arbitrary real numbers. Then the midpoint between x and y is represented by (a + b) / 2. Therefore, (a + b ) / 2 is l y - x l / 2 numbers less than
max(x, y). Then adding l y - x l / 2 to (a + b ) / 2 yields ( x + y + l y - x l / 2 = max(x, y).
Theorem. min( x, y) = (x + y - l y - x l) / 2
Proof. Let x and y be arbitrary real numbers. Then the midpoint between x and y is represented by (a + b ) /2 . Therefore, (a + b) /2 is l y - x l) / 2 greater than min(x, y). Then subtracting l y - x l) / 2 from (a + b ) / 2 yields (x + y - l y - x l) / 2 = min( x,y).
Is the reasoning in these proofs too informal? Should I instead use the trichotomy law and prove the formulas by the three cases