Proof about integers and rationals
Not what you're looking for?
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.