06-14-2012, 09:58 AM

Geometry and complex numbers are lie:

Lets consider a nail with a hole in it (1). Since complex numbers are unambiguously defined by two real numbers and so are points in a plane, consider lets an intersection of a complex plane with the nail (2). It's obvious that for every part of the space inside the nail there exists λ = Vair / Vnail, where Vnail is the volume of the nail in that part of the space and Vair is the volume of the air in that part of the space. But now consider (3), where the part of the space (green) is clearly inside the nail, but Vnail = 0, so as x/0 = ∞ there must be infinite air but this can't be. Q.E.D.

Lets consider a nail with a hole in it (1). Since complex numbers are unambiguously defined by two real numbers and so are points in a plane, consider lets an intersection of a complex plane with the nail (2). It's obvious that for every part of the space inside the nail there exists λ = Vair / Vnail, where Vnail is the volume of the nail in that part of the space and Vair is the volume of the air in that part of the space. But now consider (3), where the part of the space (green) is clearly inside the nail, but Vnail = 0, so as x/0 = ∞ there must be infinite air but this can't be. Q.E.D.