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Flashcards in Foundations of mathemtics Deck (33)
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1

N

Natural numbers {1,2,3,...}

2

Z

The set of all integers {0,+-1,+-2,+-3,...}

3

Q

The set of all natural numbers

4

R

The set of all real numbers

5

C

The set of all complex numbers {a+bi | a,b c R}

6

|u|

Number of elements in the set u

7

Singleton

A set with one element

8

The empty set

9

What is a PROPER SUBSET

Every element of B is also an element of a but b does not equal A

10

[a,b]

x is greater or equal than a, and less than or equal to b.

11

(a,b)

x is greater than a and less than b.

12

AUB

Union, x is an element of a or an element of b

13

A∩B

Intersection, x is an element of A and of B

14

A\B

Difference, x is an element of A but not an element of B

15

Disjoint

When A and B have no common elements

16

The ordered N-tuple

(x1,x2,x3,...xn) where the position of each element is significant

17

What is the cartesian product of AxB

{(a,b) | a∈A and b∈B}

18

The principle of the excluded third

either P is true, or ˜P is true, there is no third possility

19

Disjunction

P or Q (or in an inclusive sense)

20

Conjunction

P and Q

21

for every, for all

22

there exists

23

Contrapositive

if P imlies Q, it's contrapositive is that thee negation of P implies th negation of Q

24

1+2+3+....+n=?

n(n+1)/2

25

Image

The image of a function mapping A to B, is the set B

26

Domain

The domain of a function mapping A to B, is the set A

27

Injective

If a1,a2 are elements of A and a1->b and a2->b then a1=a2
(one to one function)

28

surjective

If f maps A to B every element of B is the image of at least one element of A

29

Bijective

A bijective function is both Injective and surjetive

30

Comutative

x*y=y*x