If i paint each half of a picture with a different color, which color will be in the middle?

Question

I'm asking this on logic and didn't saw anything similar anywhere else. Well let's suppose, a 100px image, 50% of it(50px) will be purple and the another 50% will be violet. Which color will be in the middle? 50% is purple and the another 50% is violet, so 100% of the image has colors.

Answer 1

In math you have to define what happens on the boundary line. If you view the square as $[0,1] \times [0,1]$ where the square brackets indicate that $0$ and $1$ are included in the interval, saying you paint the left half of the square purple and the right half violet only tells me that $[0,\frac 12)$ is purple and $(\frac 12,1]$ is violet. The language is not precise enough to say what happens exactly at the middle. You could define it either way by putting a square bracket on one of the two, or you could define that it never gets colored, or whatever you want.

In computer images you can think of there being a line between pixels (infinitely thin if you want) that never gets a color and the question does not arise.