Real number - Revision history

Sebastian at 01:16, 29 April 2022

2022-04-29T01:16:41Z

← Older revision		Revision as of 01:16, 29 April 2022
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	== Classification ==		== Classification ==

	Real numbers are classified as [[rational number]]s (denoted by ~~'''~~Q~~'''~~), [[integer]]s (~~'''~~Z~~'''~~), [[whole number]]s (~~'''~~W~~'''~~), [[natural number]]s, and [[irrational number]]s. In order of inclusion, non-irrational real numbers can be ordered as follows:		Real numbers are classified as [[rational number]]s (denoted by <math>Q</math>), [[integer]]s (<math>Z</math>), [[whole number]]s (<math>W</math>), [[natural number]]s, and [[irrational number]]s. In order of inclusion, non-irrational real numbers can be ordered as follows:

	<math>N \subseteq W \subseteq Z \subseteq Q</math>		<math>N \subseteq W \subseteq Z \subseteq Q</math>

Sebastian: /* Multiplicative inverse property */

2022-04-29T01:09:52Z

Multiplicative inverse property

← Older revision		Revision as of 01:09, 29 April 2022
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	=== Multiplicative inverse property ===		=== Multiplicative inverse property ===

	<math>a.\frac{1}{a})=1</math> where <math>a\neq0</math>		<math>a.\frac{1}{a}=1</math> where <math>a\neq0</math>

	=== Zero property of multiplication ===		=== Zero property of multiplication ===

Sebastian: /* Multiplicative inverse property */

2022-04-29T01:09:40Z

Multiplicative inverse property

← Older revision		Revision as of 01:09, 29 April 2022
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	=== Multiplicative inverse property ===		=== Multiplicative inverse property ===

	<math>a.(/frac{1}{a})=1</math> where <math>a\neq0</math>		<math>a.\frac{1}{a})=1</math> where <math>a\neq0</math>

	=== Zero property of multiplication ===		=== Zero property of multiplication ===

Sebastian: /* Substitution property */

2022-04-29T01:06:40Z

Substitution property

← Older revision		Revision as of 01:06, 29 April 2022
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	=== Substitution property ===		=== 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 ===		=== Reflexive (or identity) property of equality ===

	<math>a=a		<math>a=a</math>

	=== Symmetric property of equality ===		=== Symmetric property of equality ===

Sebastian: /* Closure property of addition */

2022-04-29T01:06:11Z

Closure property of addition

← Older revision		Revision as of 01:06, 29 April 2022
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	=== Closure property of addition ===		=== Closure property of addition ===

	<math>a+b is a real number		<math>a+b</math> is a real number

	=== Closure property of multiplication ===		=== Closure property of multiplication ===

	<math>a.b is a real number		<math>a.b</math> is a real number

	=== Addition property of equality ===		=== Addition property of equality ===

Sebastian: /* Multiplicative inverse property */

2022-04-29T01:05:50Z

Multiplicative inverse property

← Older revision		Revision as of 01:05, 29 April 2022
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	=== Multiplicative inverse property ===		=== Multiplicative inverse property ===

	<math>a.(frac{1}{a})=1</math> where <math>a\neq0</math>		<math>a.(/frac{1}{a})=1</math> where <math>a\neq0</math>

	=== Zero property of multiplication ===		=== Zero property of multiplication ===

Sebastian: /* Multiplicative inverse property */

2022-04-29T01:05:28Z

Multiplicative inverse property

← Older revision		Revision as of 01:05, 29 April 2022
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	=== Multiplicative inverse property ===		=== Multiplicative inverse property ===

	<math>a.(frac{1}{a})=1</math> where <math>~~a≠0~~</math>		<math>a.(frac{1}{a})=1</math> where <math>a\neq0</math>

	=== Zero property of multiplication ===		=== Zero property of multiplication ===

Sebastian: /* Multiplicative inverse property */

2022-04-29T01:04:16Z

Multiplicative inverse property

← Older revision		Revision as of 01:04, 29 April 2022
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	=== Multiplicative inverse property ===		=== Multiplicative inverse property ===

	<math>a.(1/a)=1</math> where <math>a≠0</math>		<math>a.(frac{1}{a})=1</math> where <math>a≠0</math>

	=== Zero property of multiplication ===		=== Zero property of multiplication ===

Sebastian at 01:01, 29 April 2022

2022-04-29T01:01:38Z

← Older revision		Revision as of 01:01, 29 April 2022
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	=== Distributive Property ===		=== Distributive Property ===

	a.(b+c)=a.b+a.c		<math>a.(b+c)=a.b+a.c</math>

	=== Commutative property of addition ===		=== Commutative property of addition ===

	a+b=b+a		<math>a+b=b+a</math>

	=== Commutative property of multiplication ===		=== Commutative property of multiplication ===

	a.(b.c)=(a.b).c		<math>a.(b.c)=(a.b).c</math>

	=== Aditive identity property ===		=== Aditive identity property ===

	a+0=a		<math>a+0=a</math>

	=== Multiplicative identiy property ===		=== Multiplicative identiy property ===

	a.1=a		<math>a.1=a</math>

	=== Multiplicative identity property ===		=== Multiplicative identity property ===

	a.1 =a		<math>a.1=a</math>

	=== Additive inverse property ===		=== Additive inverse property ===

	a+(-a)=0		<math>a+(-a)=0</math>

	=== Multiplicative inverse property ===		=== Multiplicative inverse property ===

	a.(1/a)=1 where ~~a is not 0~~		<math>a.(1/a)=1</math> where <math>a≠0</math>

	=== Zero property of multiplication ===		=== Zero property of multiplication ===

	a.0=0		<math>a.0=0</math>

	=== Closure property of addition ===		=== Closure property of addition ===

	a+b is a real number		<math>a+b is a real number

	=== Closure property of multiplication ===		=== Closure property of multiplication ===

	a.b is a real number		<math>a.b is a real number

	=== Addition property of equality ===		=== Addition property of equality ===

	If a=b, then a+c=b+c		If <math>a=b</math>, then <math>a+c=b+c</math>

	=== Substitution property ===		=== Substitution property ===

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

	=== Reflexive (or identity) property of equality ===		=== Reflexive (or identity) property of equality ===

	a=a		<math>a=a

	=== Symmetric property of equality ===		=== Symmetric property of equality ===

	If a=b, then b=a		If <math>a=b</math>, then <math>b=a</math>

	=== Transitive property of equality ===		=== Transitive property of equality ===
	If a=b and b=c, then a=c.		If <math>a=b</math> and <math>b=c</math>, then <math>a=c</math>

	=== Law of trichotomy ===		=== Law of trichotomy ===

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

Sebastian at 23:38, 28 April 2022

2022-04-28T23:38:47Z

@@ 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