(a) Show that any two open intervals (a,b) ā ā and (c,d) ā ā, where a < b and c < d are real numbers, have the same cardinality.
(b) Show that (0,1) has the same cardinality as ā (Hint: consider rational functions). Just write down a function that is a bijection; there is no need to prove your function is a bijection.
(c) Show that any open interval (a,b) ā ā where a < b are real numbers, has the same cardinality as the real numbers.