# How does this equation hold true?

The other day, I found this puzzle laying on a floor:

This holds true. Why? $$w=2u$$

There was nothing else on it. It looked like an equation of some sort, although I had no clue about the $$w$$ and $$u$$ variables. It looks somehow related to physics, maybe a magical object that always has its weight be twice its speed? Can't be sure, and it looks like I have to prove it. Prove magic? Nah. Prove something so broad without any given assumptions? Meh.

I have been staring at this equation for hours, wondering what it may represent, but to no avail; nothing came up on my mind. Eventually, I quit, so I'm posting this here. Maybe folks can figure something out, I'm literally exhausted! I'll go get some rest now, and, in the meantime, you can freely express an answer if you've figured one out, just be sure to support it with a proof.

Possible solution:

Its not so much a physics or math formula as to do with letters. The formula is saying the letter w is 2 u's as is if you put 2 u's side by side you get a w. Its even in the naming u and double-u. Since there is the lateral thinking tag I think this could be the expected solution.

• I was thinking the same thing
– Jim
Oct 24, 2018 at 20:06
• Ahh, now this sheet of paper makes more sense... yeah, how obvious, duh! I'm going to credit you with a green tick, wait a bit... :-P Oct 24, 2018 at 20:07
• Which font are you using? In every font I have seen it looks more like 2 v's than 2 u's. Which also happens to match how the letter is named in other languages. Oct 25, 2018 at 11:23
• @kasperd It appears that way more so in cursive then typed fonts and is why in English the letter is called double-u. It is a good point you make though and that's why in French the name for 'w' translates to double-v. Oct 25, 2018 at 12:04

I am going to make one assumption: $$w$$ and $$u$$ are arbitrary and can be anything. As a result, this equation may be true because it is how the variables are defined.

$$w$$ is defined as being twice as much as $$u$$. That is why $$w=2\cdot u$$.

After all, a definition of something is given to always be true. It's a self-satisfying rule.

The one major assumption here is that it is purely mathematical, as opposed to gabbo1092's more 'puzzling'-related answer.