alt Hacker NewsPrecisely. Think of mathematics like a game.
Players of magic the gathering will say a creature "has flying" by which they mean "it can only be blocked by other creatures with reach or flying".
Newcomers obviously need to learn this jargon, but once they do, communication is greatly facilitated by not having to spell out the definition.
Just like games, the definitions in mathematics are ethereal and purely formal as well, and it would be a pain to spell them out on every occasion. It stems more from efficient communication needs then from gatekeeping.
You expect the players of the game to learn the rules before they play.
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My entire being is anthithetical to this type of gatekeeping.
> You expect the players of the game to learn the rules before they play.
TFA is literally from a 'player' who has 'learned the rules' complaining that the papers remain indecipherable.
> You expect the players of the game to learn the rules before they play.
Actually, I expect to have to teach rules to new players before they play. We are different.
Well said.
I'd say the ability to take complicated definitions and to not have to through a rigorous definition every time the ideas are referenced are, in a sense a form of abstraction, and a necessary requirement to be able to do advanced Math in the first place.