Examples of Three Types of Equality - JSS1 Mathematics Lesson Note

a. Absolute Equality

Absolute equality refers to a condition where two quantities or expressions are precisely the same without any exceptions. In mathematical terms, absolute equality means that two sides of an equation are identical under all circumstances.

Example:

2𝑥=6

Here, 2𝑥 is absolutely equal to 6 when 𝑥=3.

b. Referential Equality

Referential equality, also known as identity or equivalence, means that two expressions refer to the same entity or object. In programming or mathematical logic, referential equality checks whether two references point to the same memory location or whether two mathematical expressions represent the same value, not just the same numerical result.

Example:

sin2𝜃+cos2𝜃=1

This identity holds true for all values of 𝜃

c. Conditional Equality

Conditional equality is a concept where two expressions are considered equal only under certain conditions or assumptions. This type of equality depends on specific constraints or contexts.

Example:

𝑥2=4

This equation has two solutions: 

𝑥=2 and 𝑥=−2. Therefore, 𝑥2=4 is conditionally true for 

𝑥=2 and 𝑥=−2, but not for other values of 𝑥.