[bonanova]

For real numbers x, absolute value and maximum have the following meanings:

Abs(x) is just the value of x without regard for sign: Abs(-3.3) = Abs(3.3) = 3.3

Max(x₁, x₂) is the larger of x₁ and x₂: Max(-9.2, 5.7) = Max(4.2, 5.7) = 5.7

1. Just for fun, express Abs in terms of Max.
   
2. For a bit of a challenge, express Max in terms of Abs.
   

Have fun.

[Guest]

Not sure if this is what you were looking for?

Abs(x) = Max(x, -x)

Edited February 2, 2009 by bonanova
spoler added

[Guest]

And then something like

max(x,y) = [x + y + abs(x-y)] / 2

We could add, obviously :

min(x,y) = [x + y - abs(x-y)] / 2

[Guest]

Unless I missed something

Abs = Max (-x,x) and

Max = Abs(x)

[bonanova]

And then something like

max(x,y) = [x + y + abs(x-y)] / 2

We could add, obviously :

min(x,y) = [x + y - abs(x-y)] / 2

Bingo.

[bonanova]

Unless I missed something

Abs = Max (-x,x) and

Max = Abs(x)

OK on Abs.

Max takes two arguments....

[Guest]

For real numbers x, absolute value and maximum have the following meanings:

Abs(x) is just the value of x without regard for sign: Abs(-3.3) = Abs(3.3) = 3.3

Max(x₁, x₂) is the larger of x₁ and x₂: Max(-9.2, 5.7) = Max(4.2, 5.7) = 5.7

1. Just for fun, express Abs in terms of Max.
   
2. For a bit of a challenge, express Max in terms of Abs.
   

Have fun. http://brainden.com/forum/uploads/emoticons/default_cool.png' alt='B))'>

Abs(x)=Max(x,-x)

Edited February 2, 2009 by bonanova

[bonanova]

Abs(x)=Max(x,-x)

Right.