Axioms in school mathematics

Axioms are the "universal truths" which form the basis from which mathematics evolved. In order for a student to understand how many realms of mathematics evolved, he/she needs to study and understand the different axioms in mathematics. With special reference to school curriculum, this article tries to list down the important axioms which are self-sufficiently self-explanatory. The aim of this article is to stimulate comprehension and trigger the minds of students to understand the way in which the complex structure of mathematics evolved. Keeping in mind the difficulty level of some axioms (esp. those from Groups), some topics of mathematics are deliberately omitted. The idea behind this move is that students can explore such axioms and topics at a higher level, say, in a graduate studies.

Geometry

1.Given two distinct points there is a unique line that passes through them.

2.A terminated line can be produced indefinitely.

3.A circle can be drawn with any centre and any radius.

4.All right angles are congruent.

5.If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

6.Through any point outside a line, there is exactly one parallel.

Number System

1.For any real number x, there exists a natural number y such that y is greater than x.

2.There is a set such that no set is an element of that set.

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