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implementing <> ALL (!= ALL)

\[{(a, b) \in R \vert \forall{z}\lbrack (a,z) \in S \rightarrow z \neq b \rbrack }\]

apply $ a \rightarrow b \Longrightarrow \neg a \lor \b $, we have

\[{(a, b) \in R \vert \forall{z} \lbrack (a,z) \nin S \lor z \neq b \rbrack }\]

apply $\forall{z}A \rightarrow \neg \exists{z} \neg{A}$, we have

\[{(a, b) \in R \vert \neg exists{z} \lbrack (a,z) \in S \land z \eq b \rbrack }\]

is equivalent to:

\[{(a, b) \in R \vert (a,b) \nin S }\]

on SQL

much of the success of the computer industry depends on developing a class of users other than trained computer scientists. - Donald D. Chamberlin; Raymond F. Boyce[^1]

  1. sequel-1974

mysql

removing-mysql-support We can’t support nested groups with MySQL in a performant way We have to use hacks to increase limits on columns and this can lead to MySQL refusing to store data MySQL can’t add TEXT type column without length specified MySQL doesn’t support partial indexes These limitations have already created a number of places where MySQL was already not supported (including with Geo)

postgreSQL

LATERAL JOIN

Misc