Math 308 Lecture 19 - The Schroeder Bernstein Theorem and properties of the reals and rationals

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[kstahmer]

Suppose g: [0, 1] → (0, 1) is defined by g(x) = (1/3) x + 1/3.

Then g([0, 1]) = [1/3, 2/3], not (1/3, 2/3).