You CANNOT split the closed interval [0, 1] in this way! | Set Theory Proof!

We prove that it is impossible to partition the closed interval [0, 1] into a pair of disjoint sets A and B, where B = A + x for some x. The set A + x is the translation of A and defined as A + x = {a + x : a is an element of A}. The proof is a fun application of set-theoretic ideas, and visualising subsets of the number line. The video is designed for people interested in set theory, logic, mathematical reasoning, and mathematical proof techniques such as proof by contradiction (e.g., in olympiad math, college proof-based math, real analysis etc.).

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Видео You CANNOT split the closed interval [0, 1] in this way! | Set Theory Proof! канала Math Mastery with Amitesh