I understand that the Cesaro summation is a way of assigning values to divergent sums based on the limits of averages.
Are there other approaches to assigning values?
In the case of $1+2+3+4\dots$, there is no limit to the average. So, if I am understanding right, Cesaro Summation does not assign a value for this sum.
Is there a well known principle that explains why certain values could not work as assigned values for a divergent sum?
Edit: I made a mistake in my logic so my argument is invalid. I am removing my argument which is flawed (I see no value in keeping it). If someone can assign a value to this divergent sequence or explain why no value can be assigned, I will accept that answer.