Why (-)(-)=(+)? The Question That Challenged Me When I Was in High School.

 

When I was in high school, I had a question in mind about why multiplying two negative numbers results in a positive number. I asked my teacher about it, but was told that the question was premature for my age. Undeterred, I attempted to derive the answer on my own using the following method

Step 1:

   

Also

   

 

Equations (1) and (2) serve as axioms,

To proof

   

 

Let, 

   

 

 By plugging equation (1), then

   

 

By cancelling (+) in both sides, then we obtain:

By cancelling (+) in both sides of the equation, then we obtain,

   

 

Thus, the result we obtained contradicts equation (2). Then must, 

   

 

Then Let,

   

 

By plugging equation (3),

   

 

By cancelling (-) in both sides, then we obtain:

   

 

Thus, the result we obtained contradicts equation (2). , then must,