abstractmath.org

GLOSSARY

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### obvious

A theorem is said to be obvious if the speaker’s mental representation ofmentioned in the theorem makes the truth of the fact immediately perceivable.   “Obvious” should be used carefully; you need to be sure the listener shares your particular mental representation!   See also trivial.

### order

The order of a mathematical object is a number (or other math object) associated with that object.  What “order” means depends on the mathematical specialty.

#### Examples

¨  The order of a differential equation is the highest derivative occurring in the equation.  For example the order of the equation  is 2.  Warning:  The order of  is also 2.

¨  A very common meaning for order is the cardinality of some set associated with the structure.  For example, the order of a group is the number of elements in the group.

¨  An element of a group also has an order, which is the order in the preceding sense of the cyclic subgroup it generates (it may be infinite).

¨  Degree is frequently used similarly.  Some structures, for example permutation groups, have both an order and a degree.

¨  Order can also refer to an ordering, as in “Consider the usual order on the reals.”