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I'm practicing writting a paper and for some reason it's so pleasing to write long but concise statements using just symbols.
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Strings of symbols are hard for the reader to parse, so avoid it where all possible. For example, the definition of continuity of f at a should be written

“For all e>0, there is a d>0 such that |f(x)-f(a)|<e whenever |x-a|<d”

As opposed to using symbols for “for all”, “there is” etc
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Please no. It's going to make it harder to read. Symbols are great in a lot of situations because it's more concise and more precise than natural language. But if you're going to go out of your way to type symbols, it's going to be used even in situations where it's not good, and will hurt comprehension. The book *Mathematics Made Difficult* is a satire of this and other practices that make math harder to comprehend the necessary.
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That’s kind of the essence of written language, isn’t it?
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While writing my thesis I often got comments to reduce the amount of symbols / not have multiple symbols follow another without words in between.

I adopted this and think it helps readability.
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If you want to write out the statements with symbols as a personal exercise, knock yourself out. Don't put it in a paper you intend to share with others, though.
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Aren't you supposed to do both
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When typing, the point is to communicate as clearly as possible to the reader. Too many quantifiers almost always hurts readability.

Remember:

Symbols don't equate with rigor. And what passes for rigor depends on who your target reader is.
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