/sci/ - Science & Math

>>14667236
You forgot about continuity.
Which I don't blame you for because the construction is ass.
>>14667277
Choose a space filling curve [math]f: [0, 1] \to [0, 1]^n[/math] such that [math]f(0) = f(1) = 0[/math] and a surjection [math]g: \mathbb{Z} \to \mathbb{Z}^n[/math].
Define [math]h: \mathbb{R} \to \mathbb{R}^n[/math] by [math]f(2(x - floor(x))) + g(floor(x))[/math] whenever [math]x \leq floor(x) + 0.5[/math] and by [math]g(floor(x)) + 2 (x - floor(x) - 0.5) (g(floor(x + 1) - g(floor(x))[/math] otherwise (literally a line going from[math]g(n)[/math] to [math]g(n + 1)[/math]).