Digital representation:1+2+3 = 6 =1+(2+3) = 6.

certificate

Based on piano's axiomatic system, a strict proof of the law of additive association is given by mathematical induction, where S(k) stands for the subsequent ordinal number of k, in short, S(k)=k+ 1.

To prove that (m+n)+k=m+(n+k), summarize K.

1.k=0, and (m+n)+0=m+n and m+(n+0)=m+n defined by addition, so the associative law holds for k=0.

2. Suppose the conclusion holds for k, that is, (m+n)+k=m+(n+k). The following conclusion holds for S(k).

From the definition of addition, we can get: (m+n)+s (k) = s ((m+n)+k);

And m+(n+S(k))=m+S(n+k).

=S(m+(n+k))

And through inductive hypothesis (m+n)+k=m+(n+k)

So S((m+n)+k)=S(m+(n+k))

So (m+n)+S(k)=m+(n+S(k))

So the conclusion is also true for S(k), which is proved by inductive axioms and conclusions.

For example:156+147+53 =156+(147+53)

= 156+200

=356 (simple operation)