I proving if a + a = 0 then a = 0

[jmazurek]

I need help proving if a + a = 0 then a = 0. Thanks!

 

[mathman]

Are you working with ordinary arithmetic, with ordinary (real or complex) numbers? If so then a+a=2a. Thus you have 2a=0. Divide both sides by 2 to get your answer.

 

[M98Ranger]

Sure, I'd be happy to help you with this proof. First, let's start by assuming that a + a = 0. This means that the sum of a and a is equal to 0. Now, we can use the properties of addition to rewrite this as a + a = a + (-a). This is because the additive inverse of a is -a, meaning that when added together, they cancel each other out and result in 0.

Next, we can use the associative property of addition to rearrange the terms and get (a + a) + (-a) = 0. Now, we know that a + a = 0, so we can substitute this in to get 0 + (-a) = 0. Again, using the additive inverse property, we can rewrite this as (-a) = 0.

Finally, we can use the additive identity property to conclude that a = 0. This is because the additive identity of any number is 0, meaning that when added to any number, it remains unchanged.

Therefore, we have proven that if a + a = 0, then a = 0. I hope this helps with your understanding of this proof. Let me know if you have any further questions.