I’m pretty sure appending a single number to an infinite series is not the same as appending a number to each of the terms (e.g. combining two infinite series as per my example).
But even if what you wrote were “correct” by the same token that the sum of the divergent series I mentioned is, it doesn’t have much to do my point in that paragraph, which was to say that these kind of statements make no intuitive sense but yet have some correctness to them.
I’m pretty sure appending a single number to an infinite series is not the same as appending a number to each of the terms (e.g. combining two infinite series as per my example).
But even if what you wrote were “correct” by the same token that the sum of the divergent series I mentioned is, it doesn’t have much to do my point in that paragraph, which was to say that these kind of statements make no intuitive sense but yet have some correctness to them.
They are correct if you accept a strange premise like “infinity = 0” or ignore mistakes, like the one I made in the proof above.