Real Ordering Incompatible with Subtraction

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Theorem

Let $a, b, c, d \in R$ be real numbers such that $a > b$ and $c > d$.


Then it does not necessarily hold that:

$a - c > b - d$


Proof

Proof by Counterexample:

For example, set $a = 5, b = 3, c = 4, d = 1$

Then $a - c = 1$ while $b - d = 2$.

$\blacksquare$


Sources