Prove Corollary 4.22: A set of real numbers E is closed and
bounded if and only if every infinite subset of E has a point of
accumulation that belongs to E.
Use Theorem 4.21: [Bolzano-Weierstrass Property] A set of real
numbers is closed and bounded if and only if every sequence of
points chosen from the set has a subsequence that converges to a
point that belongs to E.
Must use Theorem 4.21 to prove Corollary 4.22 and there should...
1. Prove that the Cantor set contains no intervals.
2. Prove: If x is an element of the Cantor set, then there is a
sequence Xn of elements from the Cantor set converging
to x.
Prove that if f is a bounded function on a bounded interval
[a,b] and f is continuous except at finitely many points in [a,b],
then f is integrable on [a,b]. Hint: Use interval additivity, and
an induction argument on the number of discontinuities.
Sn = (1+(1/n))^n
(a) Prove Sn is strictly increasing (b) bounded below by 2 and
above by 3
(c) Sn converges to e
(d) Obtain an expression for e
(e) Prove e is irrational
2. (a) Prove that U45 is generated by the set {14,28}.
(b) Prove that the additive group Z×Z is generated by the set
S={(3,1),(−2,−1),(4,3)}.
Please be thorough step by step with details, please.
1) Explain how to set the bar for outpatient productivity
standards.
2) List the type of outpatient records outpatient coders’ code and
identify the highest number of records coded per hour for two of
these types.