1. Decimal Fractions .
(b) In light of the last question, give me a clear way to
infinite decimal expansion that does not repeat, thus constructing
an irrational number . Be sure I can tell how to generate each digit
and also make an argument why it does not repeat.
(d) Prove that the sequence in the last question is
a sequence an is Cauchy if for any , there is a natural number
N such that if m, n > N, then )
(f) Write 0.999 . . . as the limit of a sequence of
terminating decimals .
Prove that the limit of this sequence is 1. Yes, you'll have to use
2. Comparing Set Cardinalities. Prove using the
definition of "same
size" and "fits in" in class that the following pairs of sets have the same