What is the Difference Between Factor Space and Equivalence Classes?

commutator
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FACTOR SPACE is defined in my book as the set whose elements are the equivalence classes defined by the equivalence relation R .denoted by S/R

i cannot understand where this is different from equivalent class?
page 8 - a coursein modern mathematical physics - szekeres
any help will be highly appreciated.
 
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understood. thanks.
 

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