midterm_cpe105

2. The term group was coined by _____________ around 1830 to described sets functions on finite sets that could be grouped together to form a closed set.
5. branch of discrete mathematics concerned with determining the size of finite sets without actually enumerating each element.
7. a set of distinct objects is an ordered arrangement of these objects.
12. will prove that there is a X that satisfies f(X), but does not explain how such an X will be obtained.
15. This method works by first proving the statement is true for a starting value, and then proving that the process used to go from one value to the next is valid.
17. It is a set G together with a binary operation ・ satisfying the certain axioms.
19. A property of a group that states “ If we combine any two elements in the group under the binary operation, the result is always another element in the group.”
20. A relation R on a set A is called ________

1. the probability of getting a certain value for a discrete random variable
3. If the operation is commutative, the group is called _____________________.
4. A relation R on a set A is called __________ if (a,a) R for every element a A.
6. A __________________ for a sequence {an} is an equation that expresses an in terms of one or more of the previous terms in the sequence: a0, a1, a2, …, an-1 for all integers nn0 where n0 is a nonnegative integer.
8. where it is shown that if some statement were false, a logical contradiction occurs, hence the statement must be true.
9. If k+1 or more objects are placed into k boxes, then there is at least one box containing two or more of the objects.
10. a proof in which an example is shown to exist by methods of probability theory - not an argument that a theorem is 'probably' true.
11. It is a demonstration that, given certain axioms, some statement of interest is necessarily true.
13. the result that is proved to be true
14. A _____________________ is one in which objects are defined in terms of other objects of the same type.
16. A statement which is thought to be true but has not been proven yet
18. The modern definition of the group given by both Heinrich Weber and _________ in 1882, it did not gain universal acceptance until the twentieth century.