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15.) a) Show that the real numbers between 0 and 1 have the same cardinality as...

15.)

a) Show that the real numbers between 0 and 1 have the same cardinality as the real numbers between 0 and pi/2. (Hint: Find a simple bijection from one set to the other.)

b) Show that the real numbers between 0 and pi/2 have the same cardinality as all nonnegative real numbers. (Hint: What is a function whose graph goes from 0 to positive infinity as x goes from 0 to pi/2?)

c) Use parts a and b to show that the real numbers between 0 and 1 have the same cardinality as the nonnegative real numbers.

d) Use part c and a previous result to show that the nonnegative real numbers aren't countable.

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