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hi everybody you probably know that a negative times a negative is a positive but why is that Iamp;#39;m going to show you a rigorous proof because after all what weamp;#39;re doing here is real maths follow me closely and youamp;#39;ll understand exactly whatamp;#39;s going on hey ready letamp;#39;s go you you know the old saying offices attract or if you fall and fall again it makes you stronger well todayamp;#39;s topic is a bit like that so to the maths letamp;#39;s start with a gentle warmup think about the opposite of a number in terms of its sign the opposite of negative two is two why because if you add negative two and two you get zero the neutral element and in general if you have any number a then negative a is the opposite because a plus negative a is zero to put that another way if we consider negative a then thereamp;#39;s also the number a such that when we add the two together the result is zero what does that mean from the point of view of negative a a