Question

State the Axiom of Completeness.

Answer #1

Axiom of Completeness: "Every nonempty set of real numbers that is bounded above has a least upper bound."

The **least-upper-bound property** states that
every nonempty set of real numbers having an upper bound must have
a least upper bound(or supremum) in the set of real numbers.

The rational number line **Q** does not have the
least upper bound property. An example is the subset of rational
numbers

{\displaystyle S=\{x\in \mathbf {Q} |x^{2}<2\}.}

This set has an upper bound. However, this set has no least
upper bound in **Q**: the least upper bound as a
subset of the reals would be {\displaystyle {\sqrt {2}}}, but it does not exist in
**Q** . For any upper bound *x* ∈
**Q**, there is another upper bound *y* ∈
**Q** with *y* < *x*.

how
do we prove the dedekind property implies the completeness
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Prove the Archimedian Property holds as a consequence of the
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>x.

Use Axiom of Completeness to show that the set of positive
integers that contain digit 7 in their decimal expansion (for
example, 47, 1976 or 172760) is unbounded.

Using the completeness axiom, show that every nonempty set E of
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(i.e., inf E exists and is a real number).

True or False
1. Reflexivity, completeness, and transitivity axiom ensure that
a consumer can compare one good with another.
2.More goods is preferable to less goods axiom of preferences
implies that indifference curve should be downward sloping.
3. In comparing any two bundles of goods, the consumer prefers
the one located on the indifference curve that is farthest from the
origin.
4. A thick indifference curve violates transitivity axiom of
preferences.
5. For a downward slopping linear demand curve, the...

Prove that the Egalitarian solution violates the Pareto Optimality
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Verify this axiom of a vector space.
Vector space:
A subspace of R2: the set of all dimension-2 vectors
[x; y] whose entries x and y are odd integers.
Axiom 1:
The sum u + v is in V.

Assuming Playfair’s axiom. Prove the Alternate interior angle
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180. Use these results to solve problems. Please show your work and
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why
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the precipitate washed?

Should the Federal Government follow the axiom that some
companies are "too big to fail?"
Does GM owe an ethical duty to pay the government the
money that the taxpayers lost on the bailout?
"Why" or "why not" for each question?

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