Purchase Solution

Real Analysis : Empty Set and Nested Interval Property

Not what you're looking for?

Ask Custom Question

Prove that: Intersection to infinity for n=1 (sign of intersection with infinity on top and n=1 in the bottom) of (0,1/n)=empty.
(Notice that this demonstrates that the interval in the Nested Interval Property must be closed for the conclusion of the theorm to hold.)

Purchase this Solution
Solution Summary

A real analysis problem is solved.

Solution Preview

The nested sequence of open bounded intervals,

(0,1), (0,1/2), ...

Purchase this Solution
Free BrainMass Quizzes
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

Probability Quiz

Some questions on probability

Exponential Expressions

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

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

View More Free Quizzes
Related BrainMass Solutions

  • Cantor Ternary Set : Countable or Not?

    We can construct a map f from any ternary expansion sum a_i (1/3)^i, a_i = 0,2 to the cantor set by using the nested intervals property of the real numbers. That is, any sequence a_i =0,2 defines a nested series of closed intervals I_n as follows.

  • Norms and Bounded Sets

    108646 Real Analysis : Norms and Bounded Sets 8. Fix an n-dimensional real vector space V with n a positive integer greater than 1. If you want to take V to be R, fine.

  • 24 Assorted Statistic Problems

    The bivariate correlation coefficient between the independent and dependent variables is .76. Question 17 The results of a nested ANOVA analysis indicate a statistically significant nested factor.

  • Zorn's Lemma

    Prove the real numbers, R, contain a subring A with 1 and A maximal (under inclusion) with respect to the property that 1/2 [Use Zorn's theorem].

  • Define a collection of events (FORMULA1), having the property that P(Ea)=1 for all a

    34869 Define a collection of events (FORMULA1), having the property Define a collection of events (FORMULA1), having the property that P(Ea)=1 for all a, but (FORMULA2) HINT: Let X be uniform over (0,1) and define each Ea in terms of X.

  • Problem with statistical method type

    More specifically this ANOVA would be a modified analysis of variance that has be corrected for unequal cell frequencies and accounts for nested variable differences and interactions.

  • Equal Interval Notation

    92688 Equal Interval Notation Write the sets below using interval notation. If the set is empty, write 0 .

  • Algebraic Number Theory - Definitions

    identity element under (*) [Identity property] (4) Every element of S has an inverse under (*) in S [Inverse property] Ring: A non-empty set S is said to form a ring with two binary operations * and $ (usually taken as addition and multiplication

  • Real Analysis...Open Sets

    This satisfies the definition of the open set, and hence we can safely conclude that the open interval with a, b real numbers is an open set. A real analysis for open sets are examined. The open intervals are proved.

View More Related Solutions