me: I can prove that the white square meme with any thickness black outline can't establish equality between the two colors, black and white.
Proof:
Suppose the white square has a side length of s, and the outline has a thickness of (m-s). Then the total area of the meme is m squared. The area of the entire meme is m squared. If we want to establish equality of the memes, the two areas must be equal. That means the area of the white square must be half of the meme, or in mathematical words:
s^2/m^2 = 1/2
Solving for the ratio of s to m gives us 1/sqrt(2). But from mathematical experience, we know that 1/sqrt(2) is an irrational number, and hence can't be represented as a quotient of two integers. This is a contradiction. Henceforth, we proved that the meme can't establish equality between the two colors.
also me: If one of the dimensions of the meme is an even number, we can just split it to two equal partitions, one black, one white. The proof is trivial.
