Purchase Solution

Proof about integers and rationals

Not what you're looking for?

Ask Custom Question

let x,y,z,w be rational numbers

a) Let epsilon>0. If x is epsilon-close to y, then y is epsilon-close to x.

b) Let epsilon, gamma >0. If x is epsilon-close to y, and y is gamma-close to z, then x and z are (epsilon + gamma)-close.

c) Let epsilon>0. If y and z are both epsilon close to x, and w is between y and z (i.e.. y<=w <=z or z <= w <=y), then w is also epsilon-close to x.

d) Let epsilon >0. If x and y are epsilon-close, and z is non-zero, then xz and yz are epsilon absolute value of z-close

Purchase this Solution

Solution Summary

The expert examines proofs about integers and rationals.

Solution Preview

let x,y,z,w be rational numbers

a) Let epsilon>0. If x is epsilon-close to y, then y is epsilon-close to x.
Given that x is epsilon-close to y. This implies . We know that for any rational number a, hence which implies y is epsilon-close to x.

b) Let epsilon, gamma >0. If x is ...

Purchase this Solution


Free BrainMass Quizzes
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.

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.

Solving quadratic inequalities

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

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.