Show that Multiplication of negative numbers is always positive eg. (-1)*(-1)=1
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are you allowed $-1 \cdot -1 = 1$ as a given? – stevemarvell Oct 08 '13 at 13:32
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1Relevant: http://math.stackexchange.com/questions/304422/formal-proof-for-1-times-1-1 – Arthur Oct 08 '13 at 13:37
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Define for any number $a$ the opposite of $a$ the unique number $-a$ such that $a+(-a)=0$. As $-a=a-2a=-1\cdot a$ the opposite of $a$ is achieved by multiplication of $a$ by $-1$. Hence $$-1\cdot (-1)= \text{opposite of $(-1)$}=\text{the unique number that adds up $-1$ to $0$}=1.$$
Michael Hoppe
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