tarek99 wrote:

Also, what does this expression mean when we have a minus sign?

|x-y| = |x| - |y| or

|x-y| = |y| - |x|

or, when we use the greater or less sign? for example:

|x-y| < |x| - |y|

|x-y| > |x| - |y|

I would really appreciate your input!

thanks

consider :

|x-y| = |x| - |y| or |x-y| = |y| - |x|

we are just taking difference in magnitudes or simple value (irrespective of sign )

if both x and y have same signs then above equation is true ,since the operation subtraction is subtraction if both variabl;es are of same sign.

|x-y| = |x| - |y| => this implies x,y same sign and x>y since LHS is +ve and hence RHS is +vesimilarly :

|x-y| = |y| - |x|=> this implies x,y same sign and y>x since LHS is +ve and hence RHS is +veconsider eqn:

|x-y| > |x| - |y|

this says mod of difference > diff of modes

now diff of mods is least always since max of x and max of y are subtracted.

if in case x and y have opp signs then subtraction operation becomes addition hence mod of diff of x,y with opp signs is > than actual diff of mods.

hence |x-y| > |x| - |y| => this implies x,y opp sign and x>y since LHS is +ve and hence RHS is +ve

similarly

|x-y| > |y| - |x| => this implies x,y opp sign and y>x since LHS is +ve and hence RHS is +ve|x-y| < |x| - |y| => this conmdition is not feasible since minimum diff between two numbers is the diff(in magnitude) between their mods.INVALID CONDN.
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cheers

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