## Predicate library

### Meta

This is a list of predicates together with the entries in which they are defined. So for example “$f$…functional” is a property which, according to the list below, is defined in the entry Function. Note that the list excludes certain predicates if they are named after the exact name of an entry. This is the case for some set membership predicates, So for example “$V$…vector space” is not in the list, because there is a whole entry devoted to that type of set, namely vector space. Similarly, “bijective” can be found in Bijective function.

If $x$ is a term and $\mathrm{isfoo}$ is the name of a presdicate $P$, we write “$x$ … isfoo” for $P(x)$ and “$x$ … not isfoo” or “$x$ … not an isfoo” for $\neg P(x)$.

#### Unary predicates

 Predicate Definition given in … … category Category theory … … … … computes Turing machine as partial function computes in time Turing machine as partial function … … … … … … … … countably infinite Bijective function … … … … decides Turing machine as partial function decides in time Turing machine as partial function … … … … dependent function in set theory function … … … … … … divides Natural number … … … … edge in a graph Graph … … element of a category Category theory … … equinumerous (cardinality) Bijective function … … … … … … function Function functional Function … … … … finite dimensional Vector space basis … … finite (set) Set cardinality … … … … … … holomorphic Fréchet derivative … … … … … … infinite dimensional Vector space basis … … large set Set universe … … locally euclidean space Neighbourhood … … … … … … maximal in Maximal extension in a set … … … … measurable (set) Measurable space … … … … … … smaller (cardinality) Bijective function … … small category Cat small set Set universe … … … … … … … … … … topological manifold Neighbourhood … … … … … …

#### Binary predicates

 $<, \le, >, \ge$ ordinal number, natural number, integer, rational number, real number