quiz 2 pt 2. math as language and symbols

Question 1

a system used by mathematicians to communicate mathematical ideas among themselves.

Answer 1

Language of Mathematics

Question 2

Express formulas or to represent a constant.

Answer 2

Symbols

Question 3

Facts, names, notations, or usage which are generally agreed upon by mathematicians.

Answer 3

Conventional

Question 4

To make the expression well- formed, to make characters and symbols clear, and does not violate the rules.

Answer 4

Syntax

Question 5

Characteristics of the Mathematical Language

Answer 5

Precise- able to make very fine distinction.
Concise- able to say things briefly.
Powerful - able to express complex thoughts with relative ease.

Question 6

• Combination of finite symbols that follows mathematical rules
• Correct arrangement that represents mathematical objects
• Does not have a complete thought
• Neither true nor false

Answer 6

Mathematical Expression

Question 7

• Analogue of an English sentence -
• Correct arrangement that represents a complete thought
• Use equality symbols to compare two expression
• Always true or false, sometimes true and sometimes false

complete thought

Answer 7

Mathematical Sentences

Question 8

Mathemathical Expressions:

Answer 8

Most common expressions
Numbers and Variables
Sets
Functions
Relations

Question 9

Most common sentences
-Mathematical formula
-Mathematical theories
-Mathematical postulates and -Corollaries Equations and Inequalities

Answer 9

Mathematical Sentences

Question 10

mathematical conventions

Answer 10

facts, names, notation symbols, usage

Question 11

=

Answer 11

equal sign, equality

Question 12

≠

Answer 12

not equal sign, inequality

Question 13

≈

Answer 13

approximately equal approximation

Question 14

>

Answer 14

strict inequality greater than

Question 15

strict inequality, less than

Answer 15

<

Question 16

inequality greater than or equal to

Answer 16

≥

Question 17

inequality less than or equal to

Answer 17

≤

Question 18

Grouping Symbols, calculate expression inside first

Answer 18

()/[]/{}

Question 19

caret, exponent

Answer 19

a^b

Question 20

nth root(radical)

Answer 20

n^Va

Question 21

the sum of

Answer 21

Σ

Question 22

there exists

Answer 22

∃

Question 23

for every, for all

Answer 23

∀

Question 24

element of, member of

Answer 24

∈

Question 25

not an element of

Answer 25

∉

Question 26

subset of

Answer 26

⊆

Question 27

proper subset of

Answer 27

⊂

Question 28

if…then

Answer 28

⟹

Question 29

if and only if

Answer 29

⟺

Question 30

infinity

Answer 30

∞

Question 31

can be a number, a single variable or a combination of numbers, letters and operation symbols. In algebra, we begin to see variables, or letters that are used to represent numbers,

Answer 31

Algebraic Expression

Question 32

is any letter or symbol that represents certain value. Examples: Letters of the different alphabets a, b, c, x, y, z, M, θ, β

Answer 32

Variable

Question 33

A number on its own is called a

Answer 33

constant

Question 34

is a number used to multiply a variable

Answer 34

co-efficient

Question 35

is the system of naming or representing numbers.

Answer 35

The number system or the numeral system

Question 36

is the sum of a real number and an imaginary number.

is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value ‘a’ is called the real part which is denoted by Re(z) and ‘ b’ is called the imaginary part Im(z) Also, it is called an imaginary number

Answer 36

Complex Number

Question 37

There’s no real number that gives the square root of a negative number. Suppose that I want to get the square root of-15.-15 has no square root in the set of real numbers since when a real number is multiplied by itself, the result must always be nonnegative. To express the square root of a negative number, mathematicians used imaginary numbers. They used i to represent the square root of -1. i is the basic unit of imaginary numbers or the imaginary unit.

Answer 37

Imaginary Number

Question 38

can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals, and fractions come under this category.

Answer 38

Real Number

Question 39

includes all numbers that can be written as a fraction or as a ratio of integers. However, the denominator cannot be equal to zero. A rational number may also appear in the form of a decimal. If a decimal number is repeating or terminating, it can be written as a fraction, therefore, it must be a _____________

Answer 39

Rational Number

Question 40

are numbers that cannot be written as a ratio of two integers. This description is exactly the opposite of that of rational numbers. Irrational numbers are the leftover numbers after all rational numbers are removed from the set of the real numbers. Irrational numbers if written in decimal forms don’t terminate and don’t repeat. In other words, they continue forever.

Answer 40

Irrational numbers

Question 41

includes all the elements of the set of whole numbers and the opposites or “negatives” of all the elements of the set of counting numbers. The set of negative integers is (…,-3,-2,-1). The set of positive integers is also called the set of counting numbers or natural number which is (1,2,3, and the set of whole numbers is the set of natural numbers including zero- [0,1,2,3,…).

Answer 41

Integers

Question 42

are numbers under the rational number system other than the integers. Generally, these numbers are rational fractions or decimals.

Answer 42

Non-integers