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.
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.
¨ 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.
¨ 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.”