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What is the significance of the line above the 'a' variable in this context?

What is the significance of the line above the 'a' variable in this context?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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What is the significance of the line above the 'a' variable in this context? Where the 'a' character has a horizontal line above it. 

I'm having trouble reading my textbook because I cannot find what it means. 

Since an equivalence relation is symmetric, it does not matter whether we write X ~ a or a ~ x in the definition of a. The set of things related to a is the same as the set of things to which a is related.
Transcribed Image Text:Since an equivalence relation is symmetric, it does not matter whether we write X ~ a or a ~ x in the definition of a. The set of things related to a is the same as the set of things to which a is related.
If denotes an equivalence relation on a set A, the equivalence class of an element a E A is the set a = {XEA | X a} of all elements equivalent to a. The set of all equivalence classes is called the quotient set of A mod and denoted A/~. ~ ~ ~
Transcribed Image Text:If denotes an equivalence relation on a set A, the equivalence class of an element a E A is the set a = {XEA | X a} of all elements equivalent to a. The set of all equivalence classes is called the quotient set of A mod and denoted A/~. ~ ~ ~
Expert Solution
Step 1: Definiton

Given a with bar on top equals left curly bracket x element of A space vertical line space x tilde a right curly bracket.

a is nothing but a element of A.

And the set left curly bracket x element of A space vertical line space x tilde a right curly bracketis just denoted by,a with bar on top is called the class of a. It sometimes also denoted by.left square bracket a right square bracket.


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