The First Test

Fractions and their noncomprehending learners.

So, have you ever been in a math class or having a nice discussion with someone about fractions and the topic turns to thirds? And how one third (1/3) equals 0.33333... and  two thirds (2/3) equals 0.666666... but then someone thinks that three thirds (3/3) equals 0.99999... and not 1? Well that person is an idiot.

Now they are an idiot for three main reasons that people seem to idiots on this common sense subject.
1: They think every number has a unique decimal expansion. They are wrong.
2: They might think infinitely small numbers (0.0000...01) exist. They don't they are like Unicorns
3: They might think that 0.999... terminates. It doesn't just like the original terminator.

For those who understand math there is a very simple proof by induction:
x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1

But x = 0.999...
So that means that 1 = 0.999...

Simple enough for those who understand basic math but not everyone can follow that chain of numbers and equal signs so here is an example that is much more simple to understand. Even for you Jimmy.

Say you take a bottle of water this bottle is representing one whole bottle. Pour it into three seperate glasses, so that the amount of water is exactly the same in each glass. You know that 1/3 is 0.333... and that three sets of these will be 0.333... + 0.333... + 0.333... = 0.999... But this all came from that one whole bottle so that you know 0.999... = 1. The Law of entropy does not apply in this example assume all the water is transferred from the original bottle.

Have I still not convinced you or your dumb friend? Alright how about some fancy math then.

Lets define 0.999... as an infinite series so that:

0.999... = 0 + 9(1/10) + 9(1/10)² + 9(1/10)³ ...

Now lets use a convergence theorum:

ar + ar² + ar³  + ... = ar/(1-r)

So that means:
9(1/10) + 9(1/10)² + 9(1/10)³ ... = [9(1/10)] / [1 - (1/10)]

And what does that all equal? 1 that's right Bask in the glory of understanding math and slapping that idiot who does not have common sense.

For it is required to have a super power to know and understand that 1 = 0.999...