4. As we have seen, sometimes two sets can have the same cardinality even when one...

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4. As we have seen, sometimes two sets can have the same cardinality even when one seems obviously much bigger than the other. Show that the following sets have the same cardinality. In part a, give a complete proof by finding a bijection. In part b consider our proof that the rationals are countable. (a) The interval (0, 1) and the real numbers, R (b) The integers, Z, and the Cartesian Product of the integers with itself, Z x Z 4. As we have seen, sometimes two sets can have the same cardinality even when one seems obviously much bigger than the other. Show that the following sets have the same cardinality. In part a, give a complete proof by finding a bijection. In part b consider our proof that the rationals are countable. (a) The interval (0, 1) and the real numbers, R (b) The integers, Z, and the Cartesian Product of the integers with itself, Z x Z

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