# The Reality Check #200: Favourite Segments + TRC Mistakes + Myth Recap

For a very special 200th episode the TRC crew discuss their personal favourite, and least liked, segments of the past 100 episodes. They then go over any mistakes that were uttered over the previous 100 episodes. Finally, they do a recap of all the myths debunked over the previous 100 episodes.

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### 1 Response to The Reality Check #200: Favourite Segments + TRC Mistakes + Myth Recap

1. Ian says:

Oh come on. I know this is an old show, but I can’t let it go without a comment. The 0.99999… = 1 thing? Actually pretty obvious, and the commentary against it was kiiiiind of groanworthy. You can’t just reject or object to mathematical proofs and concepts out of hand on the grounds of “nah, I personally don’t like this because it doesn’t make me feel good, so this remains a non-settled issue”, that’s beyond unsceptical and would be mocked mercilessly here if it happened in some other area of knowledge, with things like creationism and various denialists ( speaking of, endorsing that kind of thinking also leads to things like this bit of moving-the-goalpost incarnate: http://en.wikipedia.org/wiki/Ultrafinitism ). But anyway…

What does 0.1 even mean? It’s 1/10 = 1*0.1^1 (^ meaning “to the power of”)
0.05? It’s 5/100 = 5*0.1^2
0.004? It’s 4/1000 = 4*0.1^3
0.432? It’s 4*0.1^1+ 3*0.1^2 + 2*0.1^3
Zero dot 445 zeros and then a seven? 7*0.1^446.

And so, in the following the thing on the left and the thing on the right are the very same thing:
0.9 = 9*0.1^1
0.99 = 9*0.1^1 + 9*0.1^2
0.999 = 9*0.1^1 + 9*0.1^2 + 9*0.1^3
0.9999… = 9*0.1^1 + 9*0.1^2 + 9*0.1^3 + 9*0.1^4 + …

As you can clearly see from this, the expression 0.9999… doesn’t require a conversion to make it an infinite sum. It IS an infinite sum as it is already written, without us even doing anything to it. When you write it like that you can just use a simple general formula for summing up infinite geometric sequences, which goes: aq + aq^2 + aq^3 + … = aq / (1-q) with a = 9 and q = 0.1, and thus you get:
0.9999… = 9*0.1^1 + 9*0.1^2 + 9*0.1^3 + 9*0.1^4 + … = 9*0.1 / (1-0.1) = 0.9 / 0.9 = 1

It’s clear, it’s obvious after you really think about it, there’s many proofs for anyone to see, and all experts except for some small percentage of ideologically motivated cranks will tell you it’s true. Yet the lay public sees it as controversial and you’ll see wrong-but-arguing-all-the-harder-because-of-it demagogues spreading it on the internet. It is honestly not unlike the creationism “debate” in anything but the scope and location of the impact.