While driving to work I thought about a rule, problem is I don't know how to prove it.
The rule is:
For any base $B$ there will always be two palindrome numbers $A$ and $C$, whose values are: $A=(B+1), C=(B-1)$
$A$ is always $11$ - a palindrome, and $C$ will always have one digit - a palindrome.
Base Ten: (B=10, A=B+1=11, C=B-1=9); they both are palindrome.
My Question: How can I formally prove that? am I wrong?