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[PRELIMS Math] > Mathematical Languange And Symbols > Flashcards

Mathematical Languange And Symbols Flashcards

Mathematics In The Modern World Prelims Exam

1
Q

It facilitates communication and clarifies meaning.

A

Language of Mathematics

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2
Q

It allows people to express themselves and maintain their
identity

A

Language of Mathematics

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3
Q

Characteristics of the Language of Mathematics

The language of mathematics makes it easy to express the
kinds of thoughts that mathematicians like to express. It is:

A
  • Precise
  • Concise
  • Powerful
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4
Q

Mathematical Symbols

Σ

A

the sum of

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5
Q

Mathematical Symbols

Ǝ

A

there exists

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6
Q

Mathematical Symbols

ꓯ

A

for every (for any)

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7
Q

Mathematical Symbols

Є

A

element of

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8
Q

Mathematical Symbols

⊆

A

subset of

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9
Q

Mathematical Symbols

⇒

A

if …., then

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10
Q

Mathematical Symbols

⇔

A

if and only if

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11
Q

Mathematical Symbols

ℛ or ℜ or ℝ

A

set of real numbers

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12
Q

Mathematical Symbols

ℕ

A

set of natural numbers

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13
Q

Mathematical Symbols

ℤ

A

set of integers

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14
Q

Mathematical Symbols

ℚ

A

set of rational numbers

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15
Q

In English, ________ are used to name things we want to talk about (like people, places, and things); whereas sentences are used to state complete thoughts.

A

Nouns

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16
Q
  • A typical English sentence has at least _______ , and at least _____.
A

One noun
One Verb

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17
Q

MATHEMATICS: expressions versus sentences

The mathematical analogue of a ‘noun’ will be called an __________

A

Expression

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18
Q

it is a name given to a mathematical object of interest.

A

Expression

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19
Q
  • The mathematical analogue of a ‘sentence’ will also be called a _________.
A

Sentence

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20
Q

‘=‘ is

A

Verb

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21
Q

The ________ is the object that is being worked on by an operation.

A

Operand

22
Q

___________ can be mathematical ones such as multiplication or
addition, or they can be more sophisticated functions.

A

Operations

23
Q

Operations can be mathematical ones such as ______________ or _____________, or they can be more ____________ functions.

A

Multiplication
Addition
Sophisticated

24
Q

In all computer languages, expressions consist of two types of components:

A

Operators
Operands

25
Q

________ are the objects that are manipulated

A

Operands

26
Q

__________ are the symbols that represent specific actions.

A

Operators

27
Q

5 + x

x and 5 are __________
+ is an ________

A

Operands
Operators

28
Q

Types of Operators

A

Unary
Binary

29
Q

It means operation performed on one operand

A

Unary

30
Q

It means operation is performed on two operands

A

Binary

31
Q

is an operation with only one operand, i.e. a single input.

A

Unary operation

32
Q

are prefix notation (e.g. +, −, ¬), postfix notation (e.g. factorial n!), functional notation (e.g. sin x or sin(x)), and superscripts (e.g. transpose AT). Other notations exist as well.

A

Common notations

33
Q

In common arithmetic,
the unary operators are:

A

negation
reciprocal
absolute value

34
Q

____________ involves reversing the sign of a number.

A

Negation

35
Q

it involves dividing 1 by the number.

A

Reciprocal

36
Q

The _____________ involves reversing the sign of a number if it is
negative, and leaving the number unchanged if it is 0 or positive.

A

Absolute value

37
Q

a set is a calculation that combines two elements of the set (called________) to produce another element of the set.

A

Binary operation
Operands

38
Q

a______________ is an operation of parity (the number of arguments or operands that the function takes) of two whose two _____ and one _________ are the same set.

A

binary operation
domains
codomain

39
Q

PROPERTIES OF BINARY OPERATIONS

A
  1. Closure of Binary Operations
  2. Commutativity of Binary Operations
  3. Associativity of Binary Operations
  4. Distributivity of Binary Operations
  5. Identity Elements of Binary Operations
  6. Inverses of Binary Operations
40
Q

A Binary Operations that product and the sum of any two real numbers is also a real number. In symbols, we write

A

Closure of Binary Operations

41
Q

What binary operation is said to be ________ if a change in the order of the arguments results in equivalence?

A

Commutativity of Binary Operations
Commutative

42
Q

What binary operation is said to be ________ if parentheses can be reordered and the result is equivalent?

A

Associative
Associativity of Binary Operations

43
Q

________________applies when multiplication is performed on a group of two numbers added or subtracted together

A

Distributivity of Binary Operations

44
Q

An element “e” is said to be an ____________ (or neutral element) of a binary operation if under the operation any element combined with “e” results in the same element.

A

Identity Elements of Binary Operations

45
Q

For an element x, the ____ denoted x1 when combined with x under the binary operation results in the identity element for that binary operation.

A

Inverses of Binary Operations

46
Q

is an instrument for appraising the correctness of reasoning.

A

Logic

47
Q

is a declarative statement that is true or false but not both.

A

proposition P

48
Q

is a table that shows the truth value of a compound statement for all possible truth values of its simple statements.

A

Truth Table

49
Q

it is if the word is not introduced in the negative statement.

A

NEGATION

50
Q

A word or symbol that joins two sentences to produce a new one.

A

LOGICAL CONNECTIVES

[PRELIMS Math] (4 decks)

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