Show that χΔ: ℝ →ℝ, the characteristic function of the Cantor set, is discontinuous at each point of Δ. | Numerade

SOLVED: Prove by contradiction that "The Cantor Set is Uncountable"

The Cantor set, named after the German mathematician George Cantor (1845 - 1918), is constructed as follows. We start with the closed interval [0, 1] and remove the open interval ( (1)/(3), (2)/(3) ). That leaves the two intervals [ 0, (1)/(3) ] and [ (2)/(3), 1 ] and we remove the open middle third of each. Four intervals remain and given we remove the open middle third of each of them. We continue this procedure indefinitely, at each step removing the open middle third of every interval that r

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"Deconstructing Cantor's Diagonal Argument" - YouTuber misunderstands and fails to debunk a famous proof

SOLVED:Consider the set of all real numbers whose decimal expansion contains only 2 's and 7's. Using Cantor's diagonal argument, show that this set is uncount. able.