- Function
- A single output is associated with each input element drawn from a fixed set. (Also a well behaved relation).
- Relation
- A set of outputs are associated with each input element.
Functions
- Partial
- Not all inputs are mapped to an output.
- Injective
- Each input maps to one output. Not all outputs need to be mapped by an input. (Function that doesn't reach the range).
- Surjective
- Every output is mapped by at least one input. (Function that goes up and down).
- Bijective
- Injective and surjective. (Function with a monotonic gradient that doesn't flatten).
Sets
- Partial order
- Elements in the set can be related by the <e; symbol so that the reflexive, transitive and antisymmetric conditions are satisfied.
- Total order
- A partial order which also satisfies the comparative condition.
- Lattice
- A partially ordered set in which every pair of elements has a unique supremum and infimum.
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