Proof
(related to Corollary: General Associative Law)
- The general associative law follows immediately from the associativity property, using it repeatedly.
- This holds only if the number of involved elements is finite. This counterexample with an infinite number of elements might be instructive:
$$\begin{array}{rcl}(1-1)-(1-1)-(1-1)-\ldots&=&0-0-\ldots=0,\\
1-(1-1)-(1-1)-(1-1)-\ldots&=&1-0-0-\ldots=1,
\end{array}$$
therefore $$(1-1)-(1-1)-(1-1)-\ldots\neq 1-(1-1)-(1-1)-(1-1)-\ldots.$$
∎
Thank you to the contributors under CC BY-SA 4.0! 
- Github:
-
