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

Absolute value : The absolute value $|x|$ of a number $x$ is defined as the value of $x$ ignoring any potential minus sign. For example $|-2|=2$ and $|2|=2.$ In other words $|x|=x$ for $x\geq 0$ and $|x|=-x$ for $x\lt 0.$

Negative : A number is negative if it is $\lt 0.$

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

Positive : Positive means $\geq 0.$

Subtraction : Subtraction is the mathematical operation that describes decreasing a number by an amount equal to a second number. The mathematical symbol for subtraction is the minus sign $-.$ The term subtraction is also used for a generalization of this basic operation on numbers to functions, vectors and matrices.

Sum : A sum is the result of an addition.

Addition : Addition is the mathematical operation that describes increasing a number by an amount equal to a second number. The mathematical symbol for addition is the plus sign $+.$ The term addition is also used for a generalization of this basic operation on numbers to functions, vectors and matrices.

Contradiction : A contradiction is a statement that is the opposite of one of the assumptions. As not both a statement and its opposite can be true at the same time this forms the basis of proofs by contradiction.

Counterexample : A counterexample to a statement of the form 'all objects of type x have property y' is an object of type x that does not have property y. A counterexample to a statement shows that the statement is not true in general. For example the number 3 is a counterexample to the statement that all numbers are even.

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.

Multiplication : Multiplication is the mathematical operation that is a shorthand for adding the same amount several times. For example $3\cdot 4=4+4+4=12.$

Rational number : A rational number is a number of the form $\frac{a}{b}$ with integers $a, b.$

Similarity : Two shapes are called congruent if they have the same shape and size. Corresponding angles are the same in similar shapes and the ratio of corresponding side length is constant.

Square root of 2 : The square root of 2 also written as $\sqrt{2}$ is the positive number such that $(\sqrt{2})^2=\sqrt{2}\cdot \sqrt{2}=2.$ $\sqrt{2}$ is an irrational number and rounded to the nearest hundredths it is equal to 1.41.

Subtraction : Subtraction is the mathematical operation that describes decreasing a number by an amount equal to a second number. The mathematical symbol for subtraction is the minus sign $-.$ The term subtraction is also used for a generalization of this basic operation on numbers to functions, vectors and matrices.