Mathematical System Review

These are terms that are not precisely defined and are generally accepted.

• Axioms/Postulates

• Defined terms

• Theorems 

• Undefined terms 

These are terms that are defined using the undefined terms.

• Axioms

• Defined terms

• Theorems

• Undefined terms

These are statements that are taken to be true, to serve as a premise or starting point for further reasoning and arguments.

• Axioms/Postulates

• Defined terms

• Postulates 

• Undefined terms

These are statements proven based on axioms and some set of logical connectives.

• Defined terms 

• Postulates 

• Theorems

• Undefined terms 

It consists of some undefined terms (primitive terms) and a list of statements, called axioms or postulates, concerning the undefined terms to obtain a mathematical theory by proving new statements, called theorems, using only the axioms (postulates), logic system, and previous theorems.

 

• Algebraic System  

• Geometrical System

• Mathematical System

• Rectangular System