https://www.youtube.com/results?search_query=wau
According to the links above, this neat little number (which I never before heard of:dubious:) was known to the ancients.
Is it a constant like sqrt2, pi, and e, with an expressable value?
What equasions/formulas is it used in?
[spoiler]One of her expressions was:
F = 5/6 + (5/6 + (5/6 + …)/6)/6
Which is equivalent to (since that part to the upper-right is equal to F itself):
F = 5/6 + F/6
Solve:
6F = 5 + F
5F = 5
F = 1
Or is it really 0.9999…?
:)[/spoiler]
Reported.
The digamma was not only a number but a letter in ancient (pre-classical) Greek.
Wiki has the lowdown.
Assuming I’m not being whooshed:
It’s a bit of a math joke. Wau (WOW!) is the number one. Maybe not a joke exactly, as all the properties of one are true in the videos, she’s just presenting them is an obfuscated way to show how cool (WOW!) the number one is. And how strange and mystical it seems when you present it in this manner.
Y’know, as soon as I saw Dr. Strangelove refer to the video-presenter as “her”, I said to myself “I’ll bet that’s Vi Hart”.
The video is a bit trollish, but she just might succeed at tricking some folks into thinking.
On the bright side, Miss Hart is certainly making mathematics cool for young women … and that’s gotta be a good thing.
Quartz’ Wikilink gives the value of wau as six … so does that mean 0.999…∞… = 6 (= Ϝ) once we get “beyond infinity”?
I… but I didn’t mean… it was just a jo… aaaaaahhhhhh! (trapdoor to lava pit slides closed)
It’s really -…999999.0
Three’s another video that makes the argument that wau = 1 or 0, given the properties she gave. (I think there may be a couple exceptions.)
The letter wau was an actual letter of the greek alphabet which was used in many older, preclassical dialects to represent the indo-european w sound, and comes from the semitic letter of the same name. It was called digamma only after it stopped being used for a long time due to its resemblance to two gamma letters. It is the sixth leter of the greek alphabet and just signifies the number 6, nothing mystical or obscure. It lies between the letter epsilon, the number five, and the letter zeta, the number 7. Later in byzantine times the new letter stigma, an abreviation for the st consonant cluster, was used for the number six. Nowadays stigma is no longer used, and six is symbolized with st.
To be clear, the ancient use of wau to represent 6 and Vi Hart’s cheeky use of wau to represent 1 have nothing to do with each other.
(And Hart does indeed use wau to represent 1 and not 0; while a few of the properties she gives are satisfied by not just 1 but also 0 or other values, other properties she notes are satisfied only by 1, and indeed, thus 1 is the only value simultaneously satisfying ALL the properties she notes)
I disagree. I think it’s really the sum of -1 + -2 + -4 + -8 + …
“One Is The Loneliest Number” {Youtube video 3’06"}
Which is of course one of the properties of wau she mentions, that it doesn’t have a unique decimal representation. Incidentally, this is one of the properties which rules out wau=0.
Perhaps the least ambiguous property she ever notes is the straight up definition “e[sup]2iπ[/sup] = ϝ”, which is satisfied by 1 and only 1.
Unless you’re using IEEE 754. Then, negative zero is a possibility :).
Also, …9999.9999… (and for that matter …1111.1111…) and such things. 
I was leaving implicit that by “decimal representation”, I meant “according to the standard conventions for such”. I mean, I could invent a convention that 1.0 represented 0, and 2.0 represents one, and 4.0 represents two, and so on, and in that convention 0 would have two representations, but nobody would ever actually use that convention.
Yes, of course. I’m just joking around, as we all are.