Without using the Schro ?der-Bernstein theorem, find a bijection f : [0,1] ? (0,

Question

Explanation / Answer

Just map 0 -> 1/2 1 -> 1/3 1/2 -> 1/4 1/3 -> 1/5 1/4 -> 1/6 1/5 -> 1/7 ... ... This is a bijection between {0, 1} U {1/2, 1/3, 1/4, 1/5, ...} and {1/2, 1/3, 1/4, 1/5, ...}. One can just map the rest of the open unit interval to itself. --- A full description: Define f(x): [0, 1] -> (0, 1) by f(0) = 1/2 If n is a positive integer, then f(1/n) = 1/(n + 2) Otherwise (that is, if x is not zero and cannot be written in the form 1/n for n a positive integer), then f(x) = x.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.