30 Examples of Axioms

Axioms

The axioms are statements very evident, that are considered universal truths and that are used in different sciences and theories as bases to make other statements or hypothesis. For instance: Two parallel lines never touch.

As they are obvious, they do not need to be proven and cannot be deduced from other statements. Axioms are used in logic, philosophy, mathematics, physics, biology, among other disciplines.

Before the axioms were considered unquestionable truths but at present they are valid and accepted by a scientific community at a given moment and can be refuted or reformulated.

A set of axioms forms an axiomatic system, that is, a set of propositions or postulates that are used in a discipline with the aim of proving theories or theorems.

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Examples of axioms

1. Given a center and a radius, a circle can be drawn. (It belongs to the postulates of Euclid, a Greek mathematician)
2. All right angles are equal to each other. (It belongs to the postulates of Euclid, a Greek mathematician)
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3. The whole is equal to the sum of the parts. (mathematical axiom)
4. A straight line is the shortest distance between two points. (axiom of geometry)
5. Two straight lines never enclose something. (axiom of geometry)
6. Two parallel lines never touch. (axiom of geometry)
7. The addition always gives a greater number to the numbers involved in the operation. (mathematical axiom)
8. At the beginning of the universe, there were inert gases. (axiom of the Big Bang theory)
9. A set is always greater than each of its parts. (mathematical axiom)
10. In the present life only comes from life, it cannot come from inert matter. (axiom of biology)
11. The numbers are infinite. (mathematical axiom)
12. Between three points, only one straight line passes. (axiom of geometry)
13. A proposition cannot be true and false at the same time. (axiom of logic)
14. If equal amounts are added equal amounts, the results will be equal. (mathematical axiom)
15. All lines have an infinite number of points. (axiom of geometry)
16. The number 1 is not the successor of any natural number. (mathematical axiom)
17. If two natural numbers have the same successor, those two numbers are the same number. (mathematical axiom)
18. Life cannot be transferred to inert matter. (axiom of biology)
19. If the thermal state of a biosystem is disturbed, it cannot be restored. (axiom of biology)
20. Two points determine the segment of a line. (belongs to the postulates of Euclid, Greek mathematician)
21. All segments can be extended in an unlimited line in the same direction. (belongs to the postulates of Euclid, Greek mathematician)
22. The number 1 is a natural number. (mathematical axiom)
23. If a number is natural, its successor is also a natural number. (mathematical axiom)
24. For each family of nonempty sets, there is always another set that contains one element from each of these. (axiom of choice, formulated by Ernst Zermelo)
25. It is impossible not to communicate. (axiom of communication, formulated by Paul Watzlawick)
26. The content of a message depends on the relationship between sender and receiver. (axiom of communication, formulated by Paul Watzlawick)
27. Communication depends on the score. (axiom of communication, formulated by Paul Watzlawick)
28. Communication is digital and analog. (axiom of communication, formulated by Paul Watzlawick)
29. The communication relationship can be symmetrical or complementary. (axiom of communication, formulated by Paul Watzlawick)
30. All bodies maintain their state of rest or movement, except when forces are imposed on them that make their state change. (axiom of classical mechanics, formulated by Isaac Newton)

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