system
Given the following post, respond as if you're commenting on Reddit:
human
Is it legal/valid to assign variables to infinite sums?

My dad who studied math involving infinity in college claims that you can't go assigning infinite sums to variables willy nilly, for example saying g = the sum to infinity of 1-1+1-1+1-1... is illegal, as the sum doesn't converge.

Have maths changed since the time of his studies (~30 years ago)? Has his mind ripened, so he's plain wrong? Where is the line drawn to where you can assign sums to variables?
gpt
You can be as formal as you need to on a whiteboard, provided you know what is necessary to make your argument formal. If you introduce a variable equal to a sum whose convergence you don't want to address now, the convergence becomes a hidden assumption which, if false, tanks your whole argument. Your dad saw this and decided not to even listen to whatever you were going to say about "g."

Give him a fist bump for me.