Real Ordering Incompatible with Subtraction
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Let $a, b, c, d \in R$ be real numbers such that $a > b$ and $c > d$.
Then it does not necessarily hold that:
- $a - c > b - d$
For example, set $a = 5, b = 3, c = 4, d = 1$
Then $a - c = 1$ while $b - d = 2$.