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MathWorld101 > Nigger > Flashcards

Nigger Flashcards

1
Q

A fundamental dscipline that plays a critical role in various aspects of life, science and technology

A

Importance of Mathematics

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2
Q

Teaches logical reasoning, critical thinking, and ———.

A

Problem-Solving Skills

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3
Q

Core concepts of mathematics

A

Numbers
Operations
Patterns and relationships

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4
Q

The foundation of mathematics, including natural —–

A

Numbers

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5
Q

Addition, subtraction, multiplication, division, etc

A

Operations

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6
Q

Identifying and analyzing patterns to understand relationships between numbers and variables

A

Patters and relationships

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7
Q

Science and engineering:

Example: Calculating the trajectory of a spacecraft using calculus and trigonometry

Application: Engineers use mathematics to design structure, analyze data, and create simulations.

A

Applications of mathematics

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8
Q
  • A mathematician
  • Mathematics is our one and only strategy for understanding the complexity of nature
A

Ralph Abraham

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9
Q

-Mathematics is the science of quantity
-Philosopher, and polymath

A

Aristotle

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10
Q

-The science of indirect measures

A

Auguste Cosme

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11
Q

-Mathematics is the language in which God has written in the universe

A

Galielo Galilei

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12
Q

-Mathematics is the classification and study of all possible patterns and relationships

A

Walter Warwick Sawyer

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13
Q

-Mathematics is a formal system of thought or recognizing, classifying, and exploiting patterns

A

Ian stewart

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14
Q

Learning Mathematics stimulates —– development, enchancin memory, attention, and analytical abilities.

A

Cognitive Development

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15
Q

Types of variable

A

Random variable
Discrete Variable
Continous Variable
Constant Variable
Parameter Variable
Independent Variable
Dependent Variable

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16
Q

A variable that takes on different values based on the outcomes of a random process

A

Random Variable

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17
Q

A variable that can take on a finite or countable numbers of values.

A

Discrete Variable

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18
Q

A variable that can take on any value within a given range, often involving decimals

A

Continuous Variable

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19
Q

A value that does not change within a given context or equation.

A

Constant Variable

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20
Q

A variable that remains constant within a specific context but can change when the context changes.

A

Parameter Variable

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21
Q

A variable that is manipulated or chosein in an equation or function

A

Independent variable

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22
Q

A variable whose value depends on the independent variable

A

Dependent Variable

23
Q

Mathematics is not just about numbers; it is a way of thinking, a method of problem solving, and a tool for understanding the world.

A

Importance of mathematics

24
Q

Are symbols or letters used to represent numbers or other mathematical objects.

A

Variables.

25
Q

Definition of a variable:?

Purpose Of variable:?

A

A variable is a symbol used to reprsent a number

Variables enable generalazation in mathematics

26
Q

It provides of formal way to describe collection of objects and their relationships

A

Language of sets.

27
Q

A — is a collection of distinct objects considered as a whole.

A

Set

28
Q

Sets are typically denoted by curly braces.

A

Notation

29
Q

A —— is an individual object within a set.

A

Element

30
Q

Contains no elements.

A

Empty set

31
Q

Lists all elements of the set explicitly. For example B=(a,b,c)

A

Set Notation

32
Q

Types of Relation

A

Symmetric Relation
Reflexive Relation
Transitive Relation

33
Q

A relation 𝑅 R on a set 𝐴 A is called ——- if every element is related to itself. For every 𝑎 ∈ 𝐴 a∈A, ( 𝑎 , 𝑎 ) ∈ 𝑅 (a,a)∈R.

Example: The relation “is equal to” on the set of real numbers, since every number is equal to itself.

A

Reflexive Relation

34
Q

A relation 𝑅 R on a set 𝐴 A is called —— if whenever ( 𝑎 , 𝑏 ) ∈ 𝑅 (a,b)∈R, then ( 𝑏 , 𝑎 ) ∈ 𝑅 (b,a)∈R for all 𝑎 , 𝑏 ∈ 𝐴 a,b∈A.

Example: The relation “is married to” on a set of people is symmetric because if person A is married to person B, then person B is also married to person A.

A

Symmetric Relation

35
Q

A relation 𝑅 R on a set 𝐴 A is —– if whenever ( 𝑎 , 𝑏 ) ∈ 𝑅 (a,b)∈R and ( 𝑏 , 𝑐 ) ∈ 𝑅 (b,c)∈R, then ( 𝑎 , 𝑐 ) ∈ 𝑅 (a,c)∈R for all 𝑎 , 𝑏 , 𝑐 ∈ 𝐴 a,b,c∈A.

Example: The relation “is less than” (<) on the set of real numbers is transitive because if 𝑎 < 𝑏 a<b and 𝑏 < 𝑐 b<c, then 𝑎 < 𝑐 a<c.

A

Transitive Relation

36
Q

This relation is a?

X= -2, -1, 0, 4, 5
Y= 0, -2, 3, -1, -3

A

This relation is a Function

37
Q

(-2,1), (-2,3), (0,-3), (1,4), (3,1) Determine the domain/range

A

Domain/x= -2, 0, 1, 3
Range/y = 1, 3, -3, 4,

37
Q

This relation is ?

x= -3, -1, 0, 5, 5
y= 7, 5, -2, 9, 3

A

This relation is a Not Function

Because there are repititions or duplicates of x values with different y values.

38
Q

Is the set of all x or input values. We may describe it as the colleciton of the FIRST values in the ordered pairs

A

Domain

39
Q

The set of all y Output values. we may describe it as the part of the collection of the second values in the ordered Pairs

A

Range

40
Q

OBJECTS THAT WE USE IN MATH?

A

Numbers
Variables
Operations
Sets
Relations
Functions

41
Q

Properties of Real numbers

A

Closure
Commutative
Associative
Distributive
Identity + x
Inverse + x

42
Q

Definition: Given real numbers a and b (a, bE R), then 、1 a + b is a real number (a + b E R). Therefore, the set of reals is CLOSED with respect to addition. ab is a real number (ab E R). Therefore, tho set of reals is CLOSED with respect to multiplication.

A

Closure Property

43
Q

Changing the order of the numbers in addition os
multiplication will not change the result.

A

Commutative Property

44
Q

States:
a+b = b+a
Ex: 2 + 3 = 3 + 2

A

Commutative Property of addition

45
Q

States:

a+(b+c) = (a+b)+c
3+(4+5)=(3+4)+5

A

Associative Property of addition

45
Q

states:
ab = ba
*Ex. 4 x 5 = 5 x 4

A

Commutative property of multiplication

46
Q

Changing the GROUPING of the numbers in addition or multiplication will not change the result.

A

Associative Property

47
Q

States:
(ab)c= a(bc)
(2x3) x 4 = 2x (3x4)

A

Associative Property of multiplication

48
Q

Multiplication Distributes over Addition

a(b+c) = Ab+ac
3(2+5) = 3x2 + 3x5

A

Distributive Property

49
Q

There exists a unique number 0.

In other words adding zero to a number does not change its value

a+0 = a and 0+a =a

A

Additive identity property

49
Q

For each real number there exist a real number such as -a their sum is zero

IN other words opposites add to zero 0

a + (-a) = 0

A

Additive Inverse Property

50
Q

There exists a unique number 1 such that the number 1 preserves identities under multiplication

In other words multiplying a number by 1 does not change the value of the number

a x 1 = a and 1 x a = a

A

Multiplicative Identity Property

51
Q

For each number there exist a unique real number 1/a such that ther product is 1.

a x 1/a = 1

A

Multiplicative Inverse Property

MathWorld101 (3 decks)

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