[...] Unit of LENGTH. [...]

The proof is ACTUALLY incomplete because he never defined what x is (number, vector or whatever rank tensor would all fit x+x=2x). That's what an actual mathematician would complain about in the very first line.

Ok let's do math, x is height of a single jump

You understood x to be a number without question, so surely 2x=x+x (the defining property of multiplying a number something by 2) is NOT needed in the calculation.

[...]http://en.wikipedia.org/wiki/Natural_unit Ofc units can be natural if we use outside facts to define them. This is not as pronounced in this case, though, but I would still argue since literally nobody was interested in the extra height gained relative to a single jump, using the full (w/o Winger) jump height is the obvious choice.

[...] Yea, that's just gibberish...

[...] I didn't you're making shit up now. Good time for me to quit.

[...] That's the wrong way to think about it[...]

[...] I'm fine with ignoring scales in this case, but you still have to either define the as 1 [unit of scale] if you didn't define it as x. That's what I mean't with "Unless you predefined the height of a normal jump as 1 [unit of scale]".

To go back to your full previous statement "Well, surely if to you x+x=2x warrants its own line in the context of a calculation (in which btw x is completely unnecessary)" : x+x=2x indeed warrants it's own line in the context of a proof otherwise it would be incomplete.

Defining an arbitrary unit is never more natural than defining another arbitrary unit. [...]Seeing something that better fits your line of thought as more natural might be natural for you or a lot of other humans, but that doesn't mean that your way of thinking seems natural to any other person. The only reason why two different persons might think alike and therefore each others line of thoughts seems natural to the other one is that they both live in the same world so they might have experienced the same conditions in a similar way.

The way of solving the problem doesn't have to be "more natural" for the one solving the problem to be "more natural", it could also be more similar to the nature of the problem itself to be "more natural". In other words why wouldn't be the units of the world the problem comes from "more natural" than arbitrarily defined ones? Why aren't hammer units "more natural"?

Claiming that your way of thinking is the only right one, do you know the implications of this?

[...] That's the wrong way to think about it, what I would actually be doing is setting the unit of length to the non-double-jump height of the Scout. Btw a more natural scale of the problem would actually be to define the unit of length to be the full double-jump height, or "x=0.5" in your terms. What I was actually arguing for was that since the final result is a dimensionless quantity, you can just ignore scales completely.

[...] Unless you predefined the height of a normal jump as 1

[...] Well, surely if to you x+x=2x warrants its own line in the context of a calculation (in which btw x is completely unnecessary) then figuring out if better hit chance or more +damage is better to maximize your DPS must seem like a Herculean task.

[...] It is also why I don't like such RPGs, I want to play, not figure out how to optimize a build. (although in my case it would be figuring out EVs and IVs of my pokémon and maximizing them, took all the fun out of it, but I couldn't get myself to play with any less optimal setup...)