elementary set theory - Specify a bijection from [0,1] to (0,1].

A) Specify a bijection from [0,1] to (0,1]. This shows that |[0,1]| = |(0,1]|

B) The Cantor-Bernstein-Schroeder (CBS) theorem says that if there's an injection from A to B and an injection from B to A, then there's a bijection from A to B (ie, |A| = |B|). Use this to come to again show that |[0;1]| = |(0;1]|