Why Does Multiplying Two Negative Numbers Yield a Positive?

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Homework Help Overview

The discussion revolves around the mathematical concept of multiplying two negative numbers and understanding why the product is positive. The original poster is seeking a proof that if both numbers are less than zero, their product is greater than zero.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are exploring axioms related to positivity and questioning the definitions provided in a reference text. There is an attempt to clarify the implications of these definitions on the problem at hand.

Discussion Status

Some participants have offered guidance on utilizing the definitions of positivity as outlined in the reference material. There is an acknowledgment of the need to work within the framework of these definitions to approach the proof. Multiple interpretations of the definitions are being discussed, indicating an ongoing exploration of the topic.

Contextual Notes

The original poster expresses confusion regarding the definitions of positive numbers as presented in their textbook, which may impact their understanding of the problem. There is a reference to specific axioms and definitions that are under scrutiny.

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Homework Statement


prove that if a is less than zero , and if b is less than zero then ab is greater than zero.

I have been having troubles with this problem.
thanks.


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The Attempt at a Solution

 
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What have you tried so far? Do you know what axioms for positivity you can use?
 
Office_Shredder said:
What have you tried so far? Do you know what axioms for positivity you can use?

Im reading the subject in the book of Spivak and frankly I don't understand what he says.
on page 12 he defined P to be a positive number thenhe said that for a number a only one of this three equalities is correct

a=0, a is a is part of P, and - a is part of P. I don't understand the last one since he defined P as the set of all the positive numbers maybe there might be a mistake in my book though.

is there any other way to prove this theorem?
 
For example, if a=-3, then -a is in P, not a.

You're going to have to use his definition of positivity to do the problem. You can't prove that something has a certain property without using its defining features!

As a starting point: We know that a<0 and b<0 here, so (-a)>0 and (-b)>0. Try to work from here
 

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