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If the product of two numbers is nonnegative than either both are nonnegative or both are nonpositive
In trying to prove the following inequality: $0\leq ab\Longrightarrow (0\leq a\wedge 0\leq b)\vee(a\leq 0\wedge b\leq 0)$ the following proof by contradiction was tried
Proof:
Let $0\leq ab$ and let,$...
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Formal proof of: $x>y$ and $b>0$ implies $bx>by$?
Property: If $x,y,b \in \mathbb{R}$ and $x>y$ and $b>0$, then $bx>by$.
What is a formal (low-level) proof of this result? Or is this property taken as axiomatic?
The motivation for this ...
