Shared Flashcard Set

Details

Math 290
Exam 2
18
Mathematics
Undergraduate 2
10/27/2009

Additional Mathematics Flashcards

 


 

Cards

Term
least element
Definition
A number m in A is called a least element of A if x>m for every x in A.
Term
principle of mathematical induction
Definition
For each positive integer n, let P(n) be a statement. If (1) P(1) is true and (2)the implication If P(k), then p(k+1). is true for every positive integer n.
Term
relation
Definition
By a relation R from A to B we mean a subset of AxB. That is, R is a set of ordered pairs, where the first coordinate of the pair belongs to A and the second coordinate belongs to B.
Term
co domain
Definition

is the subset of A defined by:

dom R={a in A:(a,b) in R for some b in B};

Term
reflexive
Definition
A relation R defined on a set A is called reflexive if x R x for every x in A.
Term
transitive
Definition
A relation R defined on a set A is called transitive if whenever xRy and yRz, then xRz, for all x,y,z in A.
Term
equivalence class
Definition
the set consists of all elements in A that are related to a.
Term
a|b
Definition
ak=b for all k in Z.
Term
Division algorithm
Definition
If m and n greater than or equal to 2 are integers and m is divided by n, then we can this division as m = nq + r, where q is the quotient and r is the remainder. The remainder r has to be 0 less than or equal to r
Term
well-defined
Definition
If the sum(or product) of two equivalence classes does not depend on the representatives, then we say that this sum (or product) is well-defined. Ex. [a]=[b] and [c]=[d] in Z, then [a+c]=[b+d] and [ac]=[bd].
Term
image
Definition
If (a,b) is in f, then we write b=f(a) and refer to b as the image of a.
Term
equality of functions
Definition
Define two functions to be equal, written f=g, if f(a)=g(a) for all a in A.
Term
injective
Definition
If every two distinct elements od A have distinct elements w and z in A s.t. f(w)=f(z).
Term
surjective
Definition
if every element of the co domain B is the image of some element of A.
Term
identity function
Definition
For a nonempty set A, the function iA: A-A defined by iA(a)=(a) for each a is in A.
Term
associative
Definition
Composition of the functions f,g,and h is associative if the functions h o (g  o f) and (h o g) o f are equal.
Term
permutation
Definition
A permutation of a nonempty set is a bijective function on A, that is, a function from A to A that is both 1-1 and onto.
Supporting users have an ad free experience!