bobxp wrote:The key thing here is that a 2d world is infinitly small in width, not zero in width. 0 + 0 = 0, but if x is an infinitely small number, x + x > x. Which is why you cannot have two 2d figures next to one another.
This is untrue, and although the facts and mathematical reasoning show that they cannot be to their sides, this explanation is insufficient.
1/infinity=0.
Proof:
1/9=0.111...
1/9(9)=0.111...(9)
9/9=0.111...(9)
1=0.999...
thus 0.000...1=0 and in your case of x+x>x, it would be 0+0>0 which is not a true statement where x=x.
The reason why the infinitely thin soldiers cannot stand next to each other is because they have to bend in the third dimension to do so, and thus make a 2D universe in a 3D universe exist, which is forbidden with standard laws and properties.
Furthermore, the reason why our 3D existence is not fundamentally incorrect is a) because of the anthropic principle, but most importantly, b)
Because with respect to a lower dimensional space, the existence of the higher dimensional space is its "space" divided by 0.
For example a square with an area of 4 has 4 sets of infinitely stacked lines, so with respect to the line, the square has an are of 4/0. 4/0 is undefined, but when you extend it in the next dimension it infinitely covers for each unit length of the next dimension.
The length of the line with respect to the square is simply 2.