2017年1月17日 · I believe you are mixing up two slightly different questions. Each individual equivalence class consists of elements which are all equivalent to each other. That is why one equivalence class is $\{1,4\}$ - because $1$ is equivalent to $4$. We can refer to this set as "the equivalence class of $1$" - or if you prefer, "the equivalence class of $4$".

For instance if the equivalence relation $\sim$ is "having the same sex", then there are two equivalence classes in the world: boys and girls (if we forget the ambiguous cases). In the same way, if the equivalence relation is "being born the same year", then each year yields a different equivalence class of all the people from this year.

2015年4月21日 · [3]: 3 is related to 1, and 3 is also related to 3, so the equivalence class of 3 is {1,3}. [4]: 4 is related to 0, and 4 is also related to 4, so the equivalence class of 4 is {0,4}. 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.

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2019年4月7日 · Prove that this is an equivalence relation, and find the equivalence class of the number $1/3$.

Now, by definition, the equivalence class of $\{1,2,3\}$ consists of all the sets that are equivalent to $\{1,2,3\}$, so when you're done with the above, one thing remains to check: that no other subsets are equivalent to $\{1,2,3\}$. At this point, you should be able to see the relevant patterns.

2015年4月28日 · Just look at the equivalence class of ${3}$ and try to make connections .

Transitive: If student A is in the same class as student B, and student B is in the same class as student C, then student A is in the same class as student C. In the context of modular arithmetic (e.g. modulo 6), one can see that the three conditions hold. Then the integers in a certain class all have the the same reminder (modulo 6).

2019年5月15日 · Prove the following is an equivalence relation and find equivalence class of 144. 0.

2019年5月22日 · $\begingroup$ Since (1,1) is in R, 1 is related to itself (and in general x is related to itself, for every equivalence relation). For the given R, 1 is also related to 2 (and 2 is related to 1). 1 is related to no other elements (apart from 1 and 2). So the equivalence class of 1 is {1,2}.