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GLOSSARY  

 

Posted 31 December 2008

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

obvious

A theorem is said to be obvious if the speaker’s mental representation of the mathematical object mentioned 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.

only if

or

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.”