Proving 0 = -0: Axioms & Solutions

[rsaad2]

Homework Statement

prove : 0 = -0

Homework Equations

The Attempt at a Solution

 

[Office_Shredder]

What have you done so far?

 

[rsaad2]

i do not know how to go about it so that is why i posted it here.

 

[╔(σ_σ)╝]

If you multiplied both sides of the inequality by -0 and used the distributive property what would you arrive at ? Can you arrive at the same result by using -1 instead ?

 

[HallsofIvy]

The crucial question is, what axioms are you allowed to use? The "distributive law" has been suggested but that assumes that you are working in the real numbers or at least a ring in which the distributive law is true. But "0= -0" only requires the "0" element and additive inverse- you should be able to prove this in any group. What is the definition of "-0"? Is it (-1)(0) or "the additive inverse of the multiplicative identity time the additive identity" or just "the additive inverse of the additive identity"?

 

[gomunkul51]

hint:

-0 = -1 * 0

what do you know as axioms about multiplication by zero? :)