Someone recently asked me why a negative ×× a negative is positive, and why a negative ×× a positive is negative, etc. I went ahead and gave them a proof by contradiction like this: Assume (−x)⋅(−y)=−xy(−x)⋅(−y)=−xy Then divide both sides by (−x) and you get (−y)=y Since we have a contradiction, then our first assumption must be incorrect. I'm guessing I did something wrong here. Since the conclusion of (−x)⋅(−y)=(xy) is hard to derive from what I wrote. Is there a better way to explain this? Is my proof incorrect? Also, what would be an intuitive way to explain the negation concept, if there is one?
