Convention. definition style [ca-000O]

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In this document, we unify the informal mathematical language for a definition to:

Let \(X\) be a concept \(X\).

A concept \(Z\) is a set/pair/triple/tuple \((Z, \mathtt {op}, ...)\), satisfying:

1. \(Z\) is a concept \(Y\) over \(X\) under op .
2. formula for all elements in \(Z\) ( property ).
3. for each element in concept \(X\), there exists element such that formula for all elements in concept \(Z\).
4. op is called op name, for all elements in \(Z\), we have
   1. formula
   2. formula
   ( property ).

By default, \(X\) is a set, op is a binary operation on \(X\).