Free
Main form: free, adjective. Used both in a descriptive and in a limiting sense.
Related forms: freedom (the state of being free), freeness (whether or not something is free; used in the scientific contexts)
Typical use:
- Free from or free of: Indicating the absence of constraints, relations, burdens, impositions, costs. Similar words: unfettered, unconstrained
- Free to: Having the ability and permission to perform certain actions.
Mathematics
In mathematics, free is typically used in the free from relations/constraints sense, rather than in the free to act sense.
In universal algebra
In group theory
Free group: A group freely generated by a set. The elements of the group are simply words whose letters are elements of the set and their inverses, with multiplication of words being by concatenation, and where the only rules for simplifying words are the cancellation of an element and its inverse when placed adjacent to each other.
Primary subject wiki entry: Groupprops:Free group
Also located at: Wikipedia:Free group, Mathworld:FreeGroup, Planetmath:FreeGroup