Equal

Pronunciation: / ˈi kwəl/ ?

Two values are equal if they have the same value. [1] For example, a = 15, states that the variable a has the same value as 15. The symbol '=' is called the equal sign / ˈi kwəl saɪn/ and is used to show that the expression on the left is equal to the expression on the right. The equation x+2 = 5 states that when 2 is added to an unknown value x, the sum is equal to 5.

Properties of Equality for Real Numbers

Operations

NameProperty
Addition property of equalityIf a = b then a+c = b+c
Subtraction property of equalityIf a = b then a-c = b-c
Multiplication property of equalityIf a = b then a·c = b·c
Division property of equalityIf a = b and c ≠ 0 then a÷c = b÷c
Table 1: Operative properties of equality

Reflexive Property of Equality

The reflexive property of equality states that: a = a. This means that every value is equal to itself.

Symmetric Property of Equality

The symmetric property of equality states that: If a = b then b = a. A mnemonic for this property is the meaning of symmetric. A object has binary symmetry if both sides are the same. if a = b, a is the same as b, so b = a.

Transitive Property of Equality

The transitive property of equality states; if a = b and b = c, then a = c. For example, if y = x+2 and x+2 = z-4, then y = z-4. A mnemonic for this property is taken from the root word 'transit'. A transit is a mode of movement. For example, a mass transit system is a system to move masses of people. Since equality is transitive, given a = b and b = c the value of a 'transits' or moves to c.

Equivalence Relation

An equality that is reflexive, symmetrical and transitive is called an equivalence relation.

Substitution Property

The substitution property of equality states that; if two values are equal, then one can be substituted for the other in equations.

  • if a = b, then for a function F(x), F(a) = F(b);
  • if a = b, then a + c = b + c;
  • if a = b, then a - c = b - c;
  • if a = b, then ac = bc;
  • if a = b and c is not zero, then a/c = b/c.

Trichotomy Property of Real Numbers

For any two real numbers a and b, exactly one of the following is true:

More Information

  • McAdams, David. Equivalence Relation. allmathwords.org. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Equivalence%20Relation.
  • McAdams, David. Reflexive Property of Equality. allmathwords.org. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Reflexive%20Property%20of%20Equality.
  • McAdams, David. Inequality. allmathwords.org. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Inequality.

Printed Resources

Cite this article as:


Equal. 2011-06-02. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/equal.html.

Translations

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Revision History


2011-06-02: Added equal sign (McAdams, David.)
2010-01-24: Added "References" (McAdams, David.)
2008-07-14: Added substitution property. Added additional clarifying wording to all sections. Added Wikipedia and Inequality to 'More Information' (McAdams, David.)
2008-06-07: Corrected spelling (McAdams, David.)
2008-03-31: Added equivalence relation to more information (McAdams, David.)
2008-02-04: Changed javascript keyword to html (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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