i don't think that's a proper and useful definition; arithmetic theory is a collection of facts and inferential rules; but I wouldn't say that saying “1+1 equals 2� is providing information.
Proposed Change:
at least refer to what others said about it; eg Bateson defined information as “the difference that makes a difference�
The meaning here is the common meaning of the word. Per a rule to not keep words in glossary that are used in their standard dictionary defined way, we have removed 'information' from our glossary.