 2.5.1: If 1 := [a,b] and l' := [a',b'] are closedintervalsin JR,showthat 1...
 2.5.2: If S ~ JRis nonempty,showthat S is boundedif and only if there exis...
 2.5.3: If S ~ JRis a nonemptyboundedset,andIs := [infS, supS], showthat S ...
 2.5.4: In the proof of Case (ii) ofTheorem2.5.1,explainwhyx, y exist in S.
 2.5.5: Writeout the detailsof theproofof case (iv)in Theorem2.5.
 2.5.6: If II 2 122 ... 2 In 2 ... is a nested sequenceof intervalsand if I...
 2.5.7: Let In := [0, Iln] forn EN. Provethat n:lIn = {OJ.
 2.5.8: Let In := (0, Iln) for n EN. Provethat n:1 In =
 2.5.9: Let Kn := (n, 00) for n EN. Provethat n:1 Kn =
 2.5.10: With the notation in the proofs of Theorems 2.5.2 and 2.5.3, show t...
 2.5.11: Showthatthe intervalsobtainedfromthe inequalitiesin (2)forma nested...
 2.5.12: Give the two binary representations of ~ and i6' 1
 2.5.13: (a) Give the first four digits in the binary representation of t. (...
 2.5.14: Showthatif ak'bk E to, 1, "', 9} and if a+l  a2 +...+ an = b+l ...
 2.5.15: Find the decimal representation of ~. 1
 2.5.16: Express t and 129as periodic decimals. 1
 2.5.17: What rationals are represented by the periodic decimals 1.25137...1...
Solutions for Chapter 2.5: Intervals
Full solutions for Introduction to Real Analysis  3rd Edition
ISBN: 9780471321484
Solutions for Chapter 2.5: Intervals
Get Full SolutionsIntroduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Since 17 problems in chapter 2.5: Intervals have been answered, more than 2615 students have viewed full stepbystep solutions from this chapter. Chapter 2.5: Intervals includes 17 full stepbystep solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. This expansive textbook survival guide covers the following chapters and their solutions.

Absolute value of a real number
Denoted by a, represents the number a or the positive number a if a < 0.

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Combinations of n objects taken r at a time
There are nCr = n! r!1n  r2! such combinations,

Components of a vector
See Component form of a vector.

Constant term
See Polynomial function

Decreasing on an interval
A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

Deductive reasoning
The process of utilizing general information to prove a specific hypothesis

Explanatory variable
A variable that affects a response variable.

Hypotenuse
Side opposite the right angle in a right triangle.

Inequality
A statement that compares two quantities using an inequality symbol

Probability of an event in a finite sample space of equally likely outcomes
The number of outcomes in the event divided by the number of outcomes in the sample space.

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Proportional
See Power function

Quotient of complex numbers
a + bi c + di = ac + bd c2 + d2 + bc  ad c2 + d2 i

Random variable
A function that assigns realnumber values to the outcomes in a sample space.

Rational function
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

Relation
A set of ordered pairs of real numbers.

Standard form of a polynomial function
ƒ(x) = an x n + an1x n1 + Á + a1x + a0

Xmin
The xvalue of the left side of the viewing window,.

xzplane
The points x, 0, z in Cartesian space.
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