In the proof of bolzano-weierstrass theorem in R^n on page 56 of
"Mathematical Analysis" by Apostol,...
In the proof of bolzano-weierstrass theorem in R^n on page 56 of
"Mathematical Analysis" by Apostol, should the inequality be
a/2^(m-2) < r/sqrt(n) or something related to n? a/2^(m-2) <
r/2 seems not enough
Create a mathematical proof to prove the following:
Given an integer n, and a list of integers such that the
numbers in the list sum up to n. Prove that the product of a list
of numbers is maximized when all the numbers in that list are 3's,
except for one of the numbers being either a 2 or 4, depending on
the remainder of n when divided by 3.
Show in a formal mathematical proof, theoretical analysis, an
even split of an array into two subarrays which answers in the best
performance of quicksort algorithm "appraised with respect to the
running time". coding or empirical investigation are not
needed.
Show in a formal mathematical proof, theoretical analysis,
substitution method, an even split of an array into two subarrays
which answers in the best performance of quicksort algorithm
"appraised with respect to the running time". coding or empirical
investigation are not needed.
Use the Cauchy Criterion to prove the Bolzano–Weierstrass
Theorem, and find the point in the argument where the Archimedean
Property is implictly required. This establishes the final link in
the equivalence of the five characterizations of completeness
discussed at the end of Section 2.6.
Use the Cauchy Criterion to prove the Bolzano–Weierstrass
Theorem, and find the point in the argument where the Archimedean
Property is implictly required. This establishes the final link in
the equivalence of the five characterizations of completeness
discussed at the end of Section 2.6.