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,...}

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## Q

### The set of all natural numbers

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## R

### The set of all real numbers

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## C

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

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## |u|

### Number of elements in the set u

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## Singleton

### A set with one element

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## ∅

### The empty set

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## What is a PROPER SUBSET

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

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## [a,b]

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

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## (a,b)

### x is greater than a and less than b.

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## AUB

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

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## A∩B

### Intersection, x is an element of A and of B

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## A\B

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

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## Disjoint

### When A and B have no common elements

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## The ordered N-tuple

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

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## What is the cartesian product of AxB

### {(a,b) | a∈A and b∈B}

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## The principle of the excluded third

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

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## Disjunction

### P or Q (or in an inclusive sense)

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## Conjunction

### P and Q

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## ∀

### for every, for all

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## ∃

### there exists

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## Contrapositive

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

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

### n(n+1)/2

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## Image

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

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## Domain

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

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## Injective

###
If a1,a2 are elements of A and a1->b and a2->b then a1=a2

(one to one function)

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## surjective

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

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## Bijective

### A bijective function is both Injective and surjetive

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