Metric space and triangle inequality.
Not what you're looking for?
Prove that in a metric space, if C lies between A and B and O is any other point, then OC<=OA + OB. (Hint make 3 applications of the triangle inequality)
Triangle inequality: For triangle ABC AB+BC=>AC
Purchase this Solution
Solution Summary
The triangle inequality is used to prove another inequality. The applications of triangle inequality are given.
Solution Preview
Cases when C lies on the line joining AB are trivial and can
be obtained just adding the 3 equations you wrote....
and using the result that AC+BC=AB here....
The general solution is to construct a rectangle around the line joining A and B. Draw lines parallel to x and y axis from A and B.
Since C is between A and B,C lies in this rectangle.....
If O is ...
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
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