Is the Canonical Map Z to Zsubscript5 1-1 and Onto?

[Punkyc7]

Determine if the canonical map Z to Zsubscript5 is 1-1 and onto. Prove your answer


Im not sure how to prove it but I am almost positive that its onto and not 1-1. I believe it onto because Z contains all the integers and Zsubscript5 contain the equivalence classes [0] [1] [2] [3] [4]. I don't believe that its 1-1 because 0 and 5 get mapped onto [0]

 

[spamiam]

Your proof looks good to me! You might want to be a bit more explicit about being onto. That is, if I give you the equivalence class [a], what integer gets mapped to [a] by the canonical map?