Axioms are statements that are assumed true. Axioms are important to construct theorems as theorems are statements that can be proved true using axioms Remember, while solving equations in mathematics, we prove that the left-hand side is equal to the right-hand side. Every known result descends from something else; it is proven true from other facts. The one exception is axioms; we accept them without verifying them. These are universally accepted and general truths. Let’s check some everyday-life examples of axioms.
1. 0 is a Natural Number
According to Peano’s axioms, 0 is a natural number.
2. Sun Rises in the East
It is the phrase that we have been listening to and studying since our childhood. It is a fact that does not require any proof.
3. Chess Moves
Chess is an abstract strategy game that has 16 pieces with each having distinct moves. The moves of these pieces are somewhat universally accepted without any logic, for example, ‘the knight moves like so’ is a rule that is an axiom of chess, and you agree with it and assume it without question.
4. Two Parallel Lines Never Intersect Each Other
It is a fact that two parallel lines never intersect each other. They always move parallel to each other, no matter how far they go.
5. Murphy’s law
Murphy’s law states that “Anything that can go wrong will go wrong.” This is a popular North American culture axiom. This axiom connotes a somewhat pessimistic view of life, for example, we often assume that when we keep an umbrella, it never rains and vice-versa, and when queuing, we assume the other line will always move faster.
6. Probability lies between 0 to 1
Probability can never be less than 0 or more than 1. Hence, it is an axiom because it does not need to be proved.
7. A straight line may be drawn between any two points
According to the axioms of Euclidean Plane Geometry, a straight line may be drawn between any two points.
8. All right angles are equal
According to the axioms of Euclidean Plane Geometry, all right angles are equal.