Ternary Operations outside of coding?

[OMGCarlos]

I use the ternary operation in web development all the time, eg:
x = y > z ? a : b

Which reads, if x > y then a, otherwise b

I realize that it is just a shorthand for if...else statements, but even still, are there any mathematical properties associated with it? I know inequalities have special properties - for example, dividing both sides by a negative.

I recently picked up an elementary book on set theory and I keep thinking about this. It would be interesting to know that in certain cases, I can just skip the operation and automatically assign x to a-something

 

[Mark44]

I use the ternary operation in web development all the time, eg:
x = y > z ? a : b

Which reads, if x > y then a, otherwise b

I realize that it is just a shorthand for if...else statements, but even still, are there any mathematical properties associated with it? I know inequalities have special properties - for example, dividing both sides by a negative.

I recently picked up an elementary book on set theory and I keep thinking about this. It would be interesting to know that in certain cases, I can just skip the operation and automatically assign x to a-something

There aren't any mathematical properties associated with this operator. As you note, it's just a short hand way of writing if ( ... ) then (...).

Your explanation of your example is not quite right.

x = y > z ? a : b

means if y > z, then set x to a. Otherwise, set x to b.

This is equivalent to the following C code:

if (y > z)
{
   x = a;
}
else
{
   x = b;
}

In answer to your question, no, you can't skip the comparison.