Real number: Difference between revisions

Revision as of 23:38, 28 April 2022

Calculus is based in the system of real numbers and their properties.

Real numbers are classified as rational numbers (denoted by Q), integers (Z), whole numbers (W), natural numbers, and irrational numbers. In order of inclusion, non-irrational real numbers can be ordered as follows:

$N\subseteq W\subseteq Z\subseteq Q$

a.(b+c)=a.b+a.c

a+b=b+a

a.(b.c)=(a.b).c

a+0=a

a.1=a

a.1 =a

a+(-a)=0

a.(1/a)=1 where a is not 0

a.0=0

a+b is a real number

a.b is a real number

If a=b, then a+c=b+c

If a=b, then a may be substituted for b or conversely

a=a

If a=b, then b=a

If a=b and b=c, then a=c.

Exactly one of the following holds: a<b, a=b, a>b

@@ Line 22: / Line 22: @@
 a.(b.c)=(a.b).c
-=== Aditive identity peoperty ===
+=== Aditive identity property ===
 a+0=a
@@ Line 41: / Line 41: @@
 a.(1/a)=1 where a is not 0
+=== Zero property of multiplication ===
+a.0=0
+=== Closure property of addition ===
+a+b is a real number
+=== Closure property of multiplication ===
+a.b is a real number
+=== Addition property of equality ===
+If a=b, then a+c=b+c
+=== Substitution property ===
+If a=b, then a may be substituted for b or conversely
+=== Reflexive (or identity) property of equality ===
+a=a
+=== Symmetric property of equality ===
+If a=b, then b=a
+=== Transitive property of equality ===
+If a=b and b=c, then a=c.
+=== Law of trichotomy ===
+Exactly one of the following holds: a<b, a=b, a>b