In Exercises 17–22, show that the given sets of points are equivalent by establishing a one-to-one correspondence.
Show that the set of all real numbers between 0 and 1 has the same cardinality as the set of all real numbers.
HINT: Draw a semicircle to represent the set of real numbers between 0 and 1 and a line to represent the set of all real numbers, and use the method of Example 5.
(Reference Example 5)
SHOWING THAT LINE SEGMENTS OF DIFFERENT LENGTHS ARE EQUIVALENT SETS OF POINTS Show that the line segments [0, 1] and [0, 2] are equivalent sets of points.
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