The discussion revolves around proving the commutativity of addition for integers, specifically the statement that for any two integers a and b, a + b = b + a. The original poster references the property holding for natural numbers and attempts to apply it to integers.
The discussion is ongoing, with participants seeking clarification on the definitions and assumptions involved in the original poster's approach. Some guidance has been offered regarding the need to clarify the representation of integers and the definition of addition being used.
There is a suggestion that the original poster may be using a specific presentation of integers that involves ordered pairs of natural numbers, which has not been explicitly stated. This could affect the understanding of the problem and the definitions involved.
iwonde said:(x,y)+(u,v) = (u,v)+ (x,y)
What do the equations above mean? a and b are integers, not ordered pairs.iwonde said:Homework Statement
Prove that for any two integers a and b, a+b=b+a. You may use the face that this holds for natural numbers.
Homework Equations
The Attempt at a Solution
a=(x,y), b=(u,v)
iwonde said:x,y,u,v are natural numbers
a+b = (x,y)+(u,v) = (u,v)+ (x,y) = b+a
I'm not sure if my attempt was correct.
I suspect the opening poster forgot to tell us that he's working with a specific presentation of the integers -- represented as the set of ordered pairs of natural numbers modulo an equivalence relation -- along with the definition of + that he's using.Mark44 said:What do the equations above mean? a and b are integers, not ordered pairs.