Give a direct proof of the following theorem, upon which case
you can use it for future proofs. (Hint: note that we’ve called it
a corollary as in p.81, not just a theorem.) Corollary 4.12. Every
integer is even or odd.
Give a direct proof of the following theorem, upon which case
you
can use it for future proofs. (Hint: note that we’ve called it a
corollary as
in p.81, not just a theorem.)
Corollary 4.12. Every integer is even or odd.
True or False. If true, quote a relevant theorem or reason, or
give a proof. If false, give a counterexample or other
justification.
The set of irrationals in the interval (0, 1) is not
countable. (Assume the fact that the set of points in the interval
(0, 1) is uncountable.)
True or False. If true, quote a relevant theorem or reason, or
give a proof. If false, give a counterexample or other
justification.
There is a one-to-one and onto map between the open
interval (0, 1) and the open interval (4, 8).
1. Give a direct proof that if
n is an odd integers, then n3 is
also an odd integer.
2. Give a proof by contradiction that the
square of any positive single digit decimal integer cannot have
more than two decimal digits.