system
Given the following post, respond as if you're commenting on Reddit:
human
Can all mathematical operations be chalked up as complex systems of addition operations?

Is there a known proof for or against this assertion?  

Or more broadly:  What does operator theory say about the uniqueness or the necessary and sufficient condition of operators?
gpt
No!

As an example of a valid mathematical operation that can't be chalked up as a complex system of addition consider the operation the takes a number between 1 and 26 and returns the letter whose place in the alphabet corresponds to that number.  

As another example. Consider the operation that take an positive integer and returns the first letter of the integers name. (operating on 2 returns t). Both of these are perfectly valid mathematical operations than can't be chalked up as some complex system of addition.