In: Advanced Math

If the infimum of a bounded set E does not exist in E, then why must E have a limit point. And if the infimum does exist in E, why is it inconclusive?

Let sequence an be a bounded sequence and let E be the
set of subsequential limits of an. prove that E is bounded and
contains both sup E and inf E

Why Model Something That Does Not Exist?
The purely competitive firm does not exist in the real world
anymore having disappeared in the USA by the early 1930's at the
latest. The question is: so why do we model it in almost every
textbook in Economics? What use does it serve? Discuss the
relevance of the characteristics of the purely competition firm.
Can you think of other things in other fields that we model, that
do not exist anymore?

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...

Why does corporate governance reform exist?

Does a continuous random variable X exist with E(X − a) = 0,
where a is the
day of your birthdate? If yes, give an example for its probability
density function.
If no, give an explanation.
(b) Does a continuous random variable Y exist with E
(Y − b)
2
= 0, where b is
the month of your birthdate? If yes, give an example for its
probability density
function. If no, give an explanation.

Consider the equation below. (If an answer does not exist, enter
DNE.)
f(x) = e^(3x) + e^(−x)
(a)
Find the interval on which f is increasing. (Enter your answer
using interval notation.)
Find the interval on which f is decreasing. (Enter your answer
using interval notation.)
(b)
Find the local minimum and maximum values of f.
local minimum value
local maximum value
(c)
Find the inflection point. (x, y) =
Find the interval on which f is concave up. (Enter...

Does Free Will Exist?

What are the four conditions that must exist for the free
enterprise system to exist?
What are the implications of the relationship between supply
and demand?

If a set K that is a subset of the real numbers is closed and
bounded, then it is compact.

Why does sharecropping continue to exist as opposed to laborers
renting land and paying for the rent with the proceeds of their
harvest?
Sharecropping is a farming system in
which owners of the land allow others to farm it and then the
harvest is split, with some portion (let's say half) going to the
laborer and some to the land owner. Renting land (the "English
system") is an alternative in which laborers pay a fixed monetary
rent and then keep...

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