4 ms·

It's like saying 128x and 28x, considered as finite sequences of digits followed by a letter, are in the class of sequences that end in x. Except in the infini

• jganetsk 17y ago
  They also happen to be in the class of sequences that end in 8x and 28x... also definitely their own classes. So 128x is in at least 4 classes, 28x is in at least 3. Therefore it's not an equivalence relation.
  • ggchappell 17y ago
    Ah, but 8x and 28x are not different classes; they are all the same class. I think it's clearer if you describe things the way the article does. Don't say "these are the classes"; say "here is the relation". As the article says: > Call two such sequences ‘equivalent’ if they are equal after a finite number of entries. To see whether this is an equivalence relation, you only need to check whether it is reflexive, symmetric, and transitive. Figuring out what the classes are, might be interesting, but it is not necessary.
    • jganetsk 17y ago
      If an item belongs to multiple equivalence classes, then transitivity does not hold. In other words, if you show that the classes are not disjoint, then it's not an equivalence relation. 18x belongs in the 8x class, but 28x belongs in both the 28x and 8x classes.
      • jibiki 17y ago
        And 8x belongs in 28x's class, since 8x and 28x share a tail. I think the author meant for you to interpret "equal after a finite number of entries" in the more normal fashion (e.g., 123x = 456x but 1x != 111x, the prefixes have to have equal length.) But your way seems to work fine too.