A typical mathematics system has four parts: undefined terms which cannot be precisely defined but are chosen arbitrarily to facilitate development; defined terms which are defined in terms of undefined terms; axioms and postulates which are general truths that form the basis of the system; and theorems which are statements derived from successive application of axioms and previously proved statements.

1. DHANALEKSHMI P S
B Ed MATHEMATICS

2. A typical mathematics system has the following
four parts:
Undefined terms
Defined terms
Axioms and postulates
Theorems

3. Undefined Terms
In mathematical system we come across many terms
which cannot be precisely defined . In modern
mathematics we accept certain undefined terms . The
choice of the undefined terms is completely arbitrary
and generally to facilitate the development of the
structure. Eg: point, plane, number, variable , line
etc.

4. Defined Terms
We defined the other terms of the mathematical system
in terms of undefined terms.
Eg: angle, line segment , circle etc.

5. Axioms and Postulates
Early Greeks considered postulates as general
truths common to all studies and axioms as the
truths relating to the special study at hand.

6. Theorems
A statement that we arrive at by successive application of
the rule of implication to the axiom and statements
previously arrived is called theorems. For example,
Angle in a semicircle are right angles.

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