Just a note to the grad students who plan on publishing papers. This is usually what happens ;-)

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If that...

It's too painfully true (and obvious) for a comment!

f(x) is not a function (re: Vertical lines)!

God I feel like a nerd for pointing that out.

Hm... it is a function from "what happens" to "how many people read your paper". Because the domain is discrete, You can make a vertical graph to represent it! :)

That is obviously a stepwise function. Thus the vertical lines are simply placed there for readability and not actually part of the fuction. Hence, it is completely valid.

Actually f(x) is the value of the function f at x, it's a number, not a function.

{0,x⊂{gets cited by survey paper}

{1,x⊂{submit to journal}

f(x)={2,x⊂{gets published}

{3,x⊂{gets cited}