Monday, July 14, 2008

Another Youtube Conundrum

Here’s another interesting video of a false proof I found on Youtube, which shows a rather interesting argument of why 1 = 2. See if you can spot the mistake (the mistake comes in rather early!):

I'll probably post the answer when I get home from work later, so you can have a go at it while there's time. Heh.

Well, the answer is easy: you can never divide by zero, because to divide by zero really means multiplying both sides of the equation by infinity, and everyone knows that infinity isn’t a number, it’s just an indication of the tendency of a number towards huge value.

For instance, look at the following treatment:

2 > 1

Hence: 2(∞) > ∞

Does it makes sense? Well, of course not! There’s no such thing as something that is twice as infinite as another! Infinity isn’t a number, but just a limit.

Harkening back to the question, notice that we allowed b = a, which means that (b – a) = 0. And thus this step is wrong:

Reminds me that grace is God’s way of loving us infinitely as much as an infinite God can already possibly love.

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