Main post link -> http://www.youtube.com/watch?v=GFLkou8NvJo

Have a nice look at the video and comment on what you think of it? A video by Vi Hart (a Mathemusician) Does that number really exist? Or is it hypothetical? What are your views on it? From me, Its just Wow.

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## Comments

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TopNewestIt turns out that wau equals one. That's the reason why many of these sequences work. For example, take the first infinite fraction: \[\dfrac{2}{\dfrac3{\dfrac3{\dfrac3{\cdots}+\dfrac1{\cdots}}+\dfrac1{\dfrac3{\cdots}+\dfrac1{\cdots}}}+\dfrac1{\dfrac3{\dfrac3{\cdots}+\dfrac1{\cdots}}+\dfrac1{\dfrac3{\cdots}+\dfrac1{\cdots}}}}\] For simplicity, let \[x=\dfrac{1}{\dfrac3{\dfrac3{\dfrac3{\cdots}+\dfrac1{\cdots}}+\dfrac1{\dfrac3{\cdots}+\dfrac1{\cdots}}}+\dfrac1{\dfrac3{\dfrac3{\cdots}+\dfrac1{\cdots}}+\dfrac1{\dfrac3{\cdots}+\dfrac1{\cdots}}}}.\] Then we get \[x=\dfrac{1}{3x+1x}=\dfrac1{4x}\implies x^2=\dfrac14\implies x=\dfrac12,\] so \(F=2x=1\) as desired. In addition, a lot of the exponentiation infinite series crumble under the definition that \(F=1\), since \(1^{\text{anything}}=1\).

Furthermore, how legitimate is a number whose name sounds similar to the word "wow"? ;)

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Yeah. The most straightforward clue in the video that wau is 1 is that she says \(e^{2i \pi} = F\) which obviously is one.

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There were other early clues. the one with 5/6 was easy to evaluate. We get F=5/6+1/6*(F) ->F=1. That was really the moment when I went "wait a minute..."

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David A. .... VERY BRILLIANT THINKING....GREAT ........

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I have an issue with her initial definition of "wau". It appears that the continued fraction she starts with, is in fact, not convergent. As she pointed out, the partial values of the partial fraction oscillate between 1/2 and 2; so it does not converge to 1.

It would be like saying 1-1+1-1+1... = x, so 1-x = x and x = 1/2; thus making it seem like the series converges to 1/2. But this is not true under the most "normal" idea of convergence.

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The number is actually 1

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ya

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'wau'- wow...

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David A. got the answer

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Yup mate! IT"S REALLY WOW!

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