Test 3 Theorem List Flashcards Preview

TXST: Intro To Advanced Math > Test 3 Theorem List > Flashcards

Flashcards in Test 3 Theorem List Deck (20):
1

A Relation

Is any set of ordered pairs

2

A function

Is a set of ordered pairs such that no two pairs have the same first term

3

The domain

Is the set of elements that are the first term

4

The range

Is the set of elements that are the second element

5

If A is a subset of D(f), then f(A)

Is the set {f(x)|x is an element of A}

6

If B is a subset of R(f), then the pre-image of B

Is the set {x|f(x) is an element of B}

7

If S is a subset of T and T is a subset of D(f), then

f(S) is a subset of f(T)

8

If W is a subset of V and V is a subset of R(f), then

The pre-image of W is a subset of the pre-image of V

9

If the union of S and T is a subset of D(f), then

f(the union of S and T) = the union of f(S) and f(T)

10

If the union of S and T is a subset of R(f), then

The pre-image of the union of S and T = the union of the pre-image of S and the pre-image of T

11

Definition of a Segment

There exist real number a & b such that x is in the segment iff a < x < b

12

Definition of an open set

For each point p in the set S, there is a segment r such that p is in r and the r is a subset in S

13

Suppose r and s are segments such that p is in their intersection, then

The intersection of r and s is a segment

14

If S and T is open, then

Their union and intersection is open

15

Definition of cluster point

P is a cluster point of the set S if For each segment r containing p, there is an element q in S such that q is in r and q does not equal p

16

Definition of closed sets

S is closed if p is a cluster point of S and in S

17

If S has exactly 1 element, then

S is closed

18

If S and T are closed, then

Both their intersection and union are closed

19

Suppose T is closed, then

The compliment of T is open

20

If T is open, then

The compliment of T is closed