Cancellation of inequalities in floating point arithmetic
Consider the case that x and y hold the largest representable value for the current type, and z is positive infinity. By the rules of floating point arithmetics, x + y is now infinity, which isn't less than infinity. On the other hand, z - y is also infinity, which the largest representable value is less than.
Another example would be when x is very small negative, and y = z and much larger in magnitude than x. Then x + y = y = z, but z - y = 0, which is larger than x.
The examples work for your second question as well if you flip the signs of all numbers - !(l &gt; r) is nearly equivalent to l &lt;= r. NaNs break the equivalence, but those aren't useful as examples to your question anyways.