Apr 24, 2014 · 11 Equivalence classes are sets of elements which are all equivalent between them. For instance if the equivalence relation $\sim$ is "having the same sex", then there are two equivalence …

The equivalence classes of an equivalence relation are subsets of the set on which the equivalence relation is defined, such that two elements are in the same equivalence class if and only if they are …

Jul 5, 2018 · I read through the textbook definition of the equivalence class, but still cannot clearly understand what an equivalence class is. Does anyone have a good example with a definition that …

Apr 21, 2015 · Notice that the equivalence class of 0 and 4 are the same, so we can say that [0]= [4], which says that there are only three equivalence classes on the relation R.

An equivalence class IS the same as a partition, defined by using some equivalence relation. But the quotient is ALL of those equivalence classes (partitions) under that particular equivalence relation.

The notion of an equivalence class always arises when dealing with something called an "equivalence relation." So to explain the former, we'll first discuss the latter. An equivalence relation is (speaking …

Feb 26, 2014 · In most cases I can prove whether a relation is an equivalence relation or not but have no idea what "distinct equivalent classes" are. I tried to read some examples but couldn't figure out …

Feb 9, 2015 · 7 Following is an elaborate example that will help solidify the concept of partitions, equivalence classes and equivalence relations. A mathematician has quite a bit of stuff in his garage …

Dec 28, 2017 · An equivalence class is just a way of grouping objects that, though different, are the "same" in some way. $\frac {1} {3}$ and $\frac {3} {9}$ are, in fact, different under the above …

Aug 26, 2017 · I am reading about equivalence classes and I would like to make sure I understood thins properly. My book says: The set of equivalence classes under this equivalence relation [$\\pmod n$] …