Is there a proof od negative numbers?

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    Negative Numbers Proof
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Discussion Overview

The discussion revolves around the concept of negative numbers, specifically exploring the reasoning behind the multiplication of two negative numbers resulting in a positive number. Participants seek to understand and explain this mathematical property.

Discussion Character

  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant questions the proof of negative numbers and seeks clarification on the expression -a(-b) = c.
  • Another participant provides a proof that demonstrates why the product of two negative numbers results in a positive number, using algebraic manipulation.
  • A third participant expresses difficulty in logically reasoning through the concept of negative numbers.
  • A fourth participant discusses the identity of 1 and the role of -1 in changing signs, suggesting that the absolute value of (-1)(-1) equals 1.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants present different approaches and reasoning regarding the multiplication of negative numbers, with some expressing confusion and others providing proofs.

Contextual Notes

The discussion includes varying levels of understanding and reasoning about negative numbers, with some participants relying on algebraic proofs while others struggle with the concepts involved.

Who May Find This Useful

This discussion may be useful for individuals interested in foundational mathematics, particularly those seeking to understand the properties of negative numbers and their multiplication.

Geekchick
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Hi everyone!

This may be a stupid question but is there a proof of negative numbers? Specifically why does this work -a(-b)=c I was trying to explain it to someone and drew a blank.

Thanks!
 
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Are you asking why two negatives multiplied produces a positive? If so, here's a proof I once read:


Let x = ab + (-a)(b) + (-a)(-b)


Then, x = ab + -a(b-b)
= ab -a(0)
= ab - 0
= ab

However, we also have x = b(a -a) + (-a)(-b)
= (-a)(-b)

Therefore, ab = (-a)(-b). QED.

Hope that's what you wanted.
 
Thanks i just couldn't logically reason it!
 
1 is the identity and -1 can only change the sign. Since (-1) ab = -ab. Thus the absolute value of (-1)(-1) = 1. So we have only the choices (-1)(-1) = 1 or
(-1)(-1) = -1.
 

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