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October 19th, 2016, 01:53 PM  #1 
Newbie Joined: Oct 2016 From: USA Posts: 2 Thanks: 0  Isomorphism proof help
How do I show that the function Φ(x)= x is an isomorphism from R+ ,• to R+ ,• ?

October 23rd, 2016, 03:10 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,354 Thanks: 591 
It looks to me that showing that the definition of "isomorphism" applies would be the obvious thing to do! A function is an "isomorphism" from one algebraic structure, X, to another, Y, if and only if 1) It is "onetoone" and "onto". "one to one": if f(x)= f(y) then x= y. "onto": for any y in Y, there exist x in X such that f(x)= y. For any y in R, take x= y. 2) f(x+ y)= f(x)+ f(y). 3) f(x•y)= f(x)•f(y) Since f, here, is the identity function all of those are trivial! 

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