The Math is Fine, The Universe is Broken

Posted on June 5, 2013 by Evan Knowles — No Comments ↓

If something is really really really small, does it really not exist at all? You may say no, everything has a value, no matter how small or tiny it is. The joy of existence is that that which exists cannot be taken away.

You’d be perfectly free to say that of course. Philosophy and modern thinking would support you. However, according to the math of the Universe, you’d be wrong in certain cases. Sometimes things are small enough that they just don’t matter – they exceed the internal precision that the Universe works with and they disappear.

Troubled yet? Let’s have a look.

Let’s start with an $x$ that is equal to zero point nine recurring, then multiply both sides by $10$ .

$x = 0.\dot{9}$
$\Rightarrow 10x = 9.\dot{9}$

Now subtract the second equation from the first one.

$\Rightarrow 10x - x = 9.\dot{9} - 0.\dot{9}$
$\Rightarrow 9x = 9$
$\Rightarrow x = 1$

A bit of simplification later and look’t that – $0.\dot{9}$ is not just close to $1$ , it’s actually equal to it. That tiny left over fraction is insignificant in God’s eyes.