quiz 2 pt 2. math as language and symbols Flashcards
a system used by mathematicians to communicate mathematical ideas among themselves.
Language of Mathematics
Express formulas or to represent a constant.
Symbols
Facts, names, notations, or usage which are generally agreed upon by mathematicians.
Conventional
To make the expression well- formed, to make characters and symbols clear, and does not violate the rules.
Syntax
Characteristics of the Mathematical Language
Precise- able to make very fine distinction.
Concise- able to say things briefly.
Powerful - able to express complex thoughts with relative ease.
- Combination of finite symbols that follows mathematical rules
- Correct arrangement that represents mathematical objects
- Does not have a complete thought
- Neither true nor false
Mathematical Expression
- 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
Mathematical Sentences
Mathemathical Expressions:
Most common expressions
Numbers and Variables
Sets
Functions
Relations
Most common sentences
-Mathematical formula
-Mathematical theories
-Mathematical postulates and -Corollaries Equations and Inequalities
Mathematical Sentences
mathematical conventions
facts, names, notation symbols, usage
=
equal sign, equality
≠
not equal sign, inequality
≈
approximately equal approximation
>
strict inequality greater than
strict inequality, less than
<
inequality greater than or equal to
≥
inequality less than or equal to
≤
Grouping Symbols, calculate expression inside first
()/[]/{}
caret, exponent
a^b
nth root(radical)
n^Va
the sum of
Σ
there exists
∃
for every, for all
∀
element of, member of
∈
not an element of
∉
subset of
⊆
proper subset of
⊂
if…then
⟹
if and only if
⟺
infinity
∞
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,
Algebraic Expression
is any letter or symbol that represents certain value. Examples: Letters of the different alphabets a, b, c, x, y, z, M, θ, β
Variable
A number on its own is called a
constant
is a number used to multiply a variable
co-efficient
is the system of naming or representing numbers.
The number system or the numeral system
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
Complex Number
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.
Imaginary Number
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.
Real Number
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 _____________
Rational Number
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.
Irrational numbers
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,…).
Integers
are numbers under the rational number system other than the integers. Generally, these numbers are rational fractions or decimals.
Non-integers
