Purchase Solution

Limit Inferior

Not what you're looking for?

Ask Custom Question

Suppose a_n >0 for each n in N and lim inf (a_n) > 0. Prove there is a number a>0 st a_n >/= a for all n in N. (limit n--> infinity)

Purchase this Solution
Solution Summary

A limit inferior proof is provided. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Solution Preview

Proof:
Since b=lim inf(a_n)>0, then we can find some N>0, such that |inf(a_n)-b|<b/2 for all n>N. This implies that inf(a_n)>b/2 ...

Purchase this Solution
Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

View More Free Quizzes
Related BrainMass Solutions

  • Cauchy Sequence and Limit Supremum

    70587 Cauchy Sequence and Limit Supremum Suppose that {a_n}_n is a real Cauchy sequence. Prove that lim superior n--> infinity (a_n) = lim inferior n--infinity (a_n) so as to conclude that lim n--infinity (a_n) exists.

  • Communist Economic Systems

    Another way consumers may be paying for these goods are the increased price of using these goods if the good is actually inferior and a superior good is not produced due to government regulation.

  • Budgets, Income Elasticity of Demand and Tragedy of Commons

    On the other hand the demand of inferior good increases when the income decreases whereas the demand for inferior goods decreases when the income increases. In strict economic terms children are inferior goods.

  • Proof that uses limiting values of functions

    475631 Proof that uses limiting values of functions Propose a definition for limit superior lim sup_x-->x_0;x belonging to E of f(x) and limit inferior lim inf_x-->x_0; x belonging to E of f(x) and then propose an analogue of the following for your definition

  • Market elasticity

    IF the economy is slow, income of people will decrease and thus, they will buy more inferior products such as the one sold at dollar stores.

  • Gun Control Essay

    Racism also involves the belief that certain individuals are inherently emotionally inferior, which means that the individuals of the supposedly inferior races are more likely inclined to act out of anger or other emotions instead of rational thought.

  • Why are there differences between normal and inferior goods?

    Inferior goods are not necessarily inferior per se; it's a term that economists use for goods that have a better or more desirable or more modern substitute available. E.g. black and white TVs are inferior, and a color TV is preferred.

  • Normal and Inferior goods

    Such behavior is observed due to the affordability to buy costly substitutes not the quality of inferior goods. Income elasticity of inferior goods is negative. Potato, pork or beans are suitable examples of inferior goods.

  • Slavery and Race Relations

    In terms of race relations, like the Northerners, Blacks were considered inferior to white people.

View More Related Solutions