Count : To count means to find out the number of objects by adding one for every object.

Number : A number $x$ is a mathematical symbol representing a quantity.

Division : Division is the mathematical operation that divides objects equally into groups. More generally $x\div y$ is defined as the number that if multiplied by $y$ equals $x.$

Standard algorithm : By standard algorithm we refer to any one of the algorithms that are commonly taught at school to add, subtract, multiply or divide multi-digit numbers such as long division and partial products multiplication.

Decimal : A decimal is a number represented by digits in front and after a decimal point. In front of the decimal point the digits are the ones digit, tens digit, hundreds digit and so on. After the decimal point there are the tenths digit, hundredths digit, thousandths digit and so on. For example the decimal 1.3 can be written as $1\frac{3}{10}.$

Infinity : Infinity or $\infty$ represents a number that is bigger than all numbers in $\mathbb{R}.$

Irrational number : An irrational number is a real number that can not be written as a fraction. $\sqrt{2}$ and $\pi$ are examples of irrational numbers.

One ninth : One ninth is the number $\frac{1}{9}=0.\overline{1}.$

Period : A decimal is called periodic with period $a_1a_2,\ldots,a_n$ if the sequence $a_1a_2,\ldots,a_n$ keeps on repeating forever in the decimal. For example $\frac{1}{3}=0.3333\ldots=0.\overline{3}$ has a period equal to 3. A function $f$ is called periodic with period $a$ if $f(x+a)=f(x)$ for all $x.$

Square : A square is a quadrilateral with four right angles and four equal length sides. A square is a special case of a rectangle and a special case of a rhombus.

Square root : The square root of $x$ denoted by $\sqrt{x}$ is the positive number such that $(\sqrt{x})^2=\sqrt{x}\cdot \sqrt{x}=x.$ For example $\sqrt{9}=3.$