Why is wau not equal to one?

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As said in this video below, https://www.youtube.com/watch?v=GFLkou8NvJo

The number 1 satisfies every single property of wau.

eg: first answer by Patrick Yu in the below question:

https://www.quora.com/What-is-the-number-Wau

So what's so special about wau? Isn't it equal to one?

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What Vi Hart did was pretty much the same as what the people behind dihydrogen monoxide (written out, it looks like H$_2$O) did. She just hid the name behind something really cool sounding as a joke.