## Monday, July 14, 2008

Well well, look what I found on Youtube:

It's a false proof by the way: can you spot the mistake? :p

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If you haven't figured it out, here's the explanation. The mistake lies in the very first line, where we have:

Now it makes sense that the right hand side involves a square root of (-1) squared - now a square root of something that is squared, immediately yields back itself, as such:

And so:

So how can you even write this first line down? It is a fallacy and not even an identity to start with! In fact, this is one of the problems Secondary School kids and JC kids struggle with. Do you know that what goes into the square root sign is important?

If you don't know what goes into the square root sign, then we can say both positive and negative answers are ok; but if you know that what goes inside is positive for sure, or negative for sure, then obviously the answer must be positive, or negative, and not both! I've shown this below for you to see:

So now, can we say that this is true:

Of course not! The left hand side has (-1) as its ingredients, and it is made explicit, and the right hand side has (1) as its ingredient, and it is made explicit as well. So how can you say that they're equal!

Don't get conned kids! :p