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October 19th, 2016, 01:53 PM   #1
AR1
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Isomorphism proof help

How do I show that the function Φ(x)= x is an isomorphism from R+ ,• to R+ ,• ?
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October 23rd, 2016, 03:10 AM   #2
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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 "one-to-one" 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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