Corner : A corner of a shape is a point in the shape such that this point does not lie on the line segment between any two other points in the shape. Every triangle has 3 corners and every quadrilateral has 4 corners.

Cube : A cube is a three-dimensional shape with 6 faces that are all squares. A cube has 8 corners and 12 edges.

Face : In mathematics a face of a 3-dimensional shape is any of the two-dimensional shapes that form the boundary of the three-dimensional shape. For example the 6 faces of a cube are 6 squares.

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

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.

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.

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

Non-zero : Not equal to the number 0.

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

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.