Real number: Difference between revisions

Revision as of 01:06, 29 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:

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

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

$a + b = b + a$

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

$a + 0 = a$

$a . 1 = a$

$a . 1 = a$

$a + (- a) = 0$

$a . (/ f r a c 1 a) = 1$ where $a \neq 0$

$a . 0 = 0$

$a + b$ 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 60: / Line 60: @@
 === Substitution property ===
-If <math>a=b, then a may be substituted for b or conversely
+If <math>a=b</math>, then <math>a</math> may be substituted for <math>b</math> or conversely
 === Reflexive (or identity) property of equality ===
-<math>a=a
+<math>a=a</math>
 === Symmetric property of equality ===