The Order Axioms
Not what you're looking for?
Use the field and order axioms to prove the following proposition:
If xy > 0, then either x > 0 and y > 0, or x < 0 and y < 0.
Please explain stepwise.
Purchase this Solution
Solution Summary
The Order Axioms are depicted.
Solution Preview
The Order Axioms are listed here, for example: http://math.wikia.com/wiki/Real_number#Order_axioms
We will use the property of the field:
For any x, we have (-1)x=-x, the opposite of x.
Proof: x+(-1)x = 1x+(-1)x = (1-1)x = 0x = 0
Suppose, xy>0.
By the Totality Axiom, either
a) x=0, but then xy = 0y = 0, ...
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.
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.
Probability Quiz
Some questions on probability
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts