The basic idea of calculus Part.1

Real Number System simply has three properties :

• The algebraic properties
• The completeness properties
• The order properties

The algebraic nature of the real number which enables the real numbers to commit different calculations and produce more real numbers under the usual rules.

The completeness is the essential idea of the limit. Roughly speaking, you just can't see the holes or gaps in the real number line. Naturally, without this substance it will cause the crash of the calculus.

The order properties , which is the fundamental of the inequality. let's list a example :

• a>b --> a+c>b+c

so that's the source of the inequality and also simple enough to understand. Just as the title , the basic idea, which means it's concrete to comprehend.