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Sunday, July 27, 2008

CompSys705 homework

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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