zero-sharp2 hours ago
You encounter abusive language/notation basically everywhere in math. Open up a calculus/real analysis textbook. A lot of the old ones write sequences in the curly brace/set {x_n} notation:
"let {x_n} be a sequence"
As the author points out, a sequence is a function. The statement {x_n} is the set of terms of the sequence, its range. A function and its range are two different things. And also sets have no ordering. It might seem like a minor thing, but I thought we were trying to be precise?
A second example: at the high school level, I'm pretty sure a lot of textbooks don't carefully distinguish between a function and the formula defining the function very well.
The author of this web page has a section on what he calls "double duty definitions". Personally, I don't find anything wrong with the language "let G=(V,E) be a graph". G is the graph and we're simultaneously defining/naming its structure. So, some of this is a matter of taste. And, to some extent, you just have to get used to the way mathematicians write.
[deleted]an hour agocollapsed
tpoacher2 hours ago
Very nice. I wish people put this kind of careful thought in academic manuscripts.
The whole point of introducing a math equation in a paper is to serve as a completely unambiguous formalism, devoid of the ambiguities of the spoken word.
And yet, it is all too common to read something many times and not make sense of it, until it hits me the author means something completely different than what the symbols would imply in principle, and what looked like a formalism is basically a sloppy direct translation of words as math symbols, combined with abuse of notation, idiomatic but undefined uses of established notation, or outright nonsense.
huflungdung3 hours ago
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