Zum Schein nämlich steht das Ausdruckslose, wiewohl im Gegensatz,
doch in derart notwendigem Verhältnis, daß eben das Schöne, ob auch
selber nicht Schein, aufhört ein wesentlich Schönes zu sein, wenn der
Schein von ihm schwindet.
— Walter Benjamin, “Goethes Wahlverwandschaften”, 1925
No identity for , so it can't be a rng or a semiring
Associativity and commutativity are given for both and
Neither have inverses
Only has an identity, so it can't be a near-ring (but we also can't make a rng or semiring because doesn't distribute over )
Therefore, because is the nicer structure, .
(I'm not super confident about the arguments above, maybe I missed a structure. If so, please tell me!)
Setting operator precedence and passing arguments to functions is done with parentheses , sets are denoted using , and is sometimes used in the context of statistics (variance of a variable, mean of a variable, and so on). These are not mixed.
for .
For function definitions, use instead of , e.g. instead of
In multiplication of reals (and maybe complex numbers), I prefer central dots , and sometimes concatenation . Rarely asterisks , but I try to avoid them.
I write the expectation of the probability distribution as and the variance of as . Unfortunately, is already taken for the complex numbers, so I am forced to write for the covariance, and for the correlation.
(Or social choice theory/decision theory/utility theory…)
Some people use instead of . I often don't.
As per Wikipedia, the term "maximin" refers to the strategy of maximizing one's own minimum payoff in non-zero-sum games, while "minimax" is the strategy of minimizing the opponent's maximum payoff in zero-sum games
In zero-sum games, minimizing the opponent's maximum payoff is equivalent to maximizing one's own minimum payoff
This is unfortunately asymmetric: What term would we use if we wanted to minimize our own maximum?
Looking at this symmetrically, it would create a set of strategies (some nonsensical):
(Optimizing one's own value)
Maximum
Minimum
maximize
maximax
maximin
minimize
minimax
minimin
(Optimizing the other player's value)
Maximum
Minimum
maximize
maxmaxi
maxmini
minimize
minmaxi
minmini
(This is not the terminology I will use, but I would if I were brave enough)
Start with the integers , and then specify when one wants only the positive numbers (), the positive numbers with 0 (), the negative numbers () and the negative numbers with 0 (). That would be much nicer than using , since is a commutative ring under addition and multiplication.
Treat and as idempotent operators for making expressions negative and positive, and sign flipping being done by explicitely multiplying with .
Use more different symbols from many different scripts. Sure, よ for the Yoneda embedding and Ш for the Tate-Shafarevich group or the Dirac comb are cute, but what about இ, ᚠ, ཧ, ದ, 𖤶 ,ᕚ and the entire Yi script? One might want to object that these are hard to remember and therefore pronounce correctly, which is one of the reasons I don't use them. But on the other hand, one could focus on one script at a time, making it easier to learn the different symbols, especially if they are mostly used in text.
Basically every usage of feels weird to me (except for the norm and space maybe). It often seems too important/out of place for a simple variable (or, god forbid, an index).