(08/30/2012, 05:24 PM)JmsNxn Wrote: Well. The reason I ask is because I was structuring my semi operators around the distribution of the set:Sorry if my question is stupid (I'm a newbie in math) but I'm a bit confused.

claim that there are operators unique to x and y which allow us to perform operations on elements of instead of operations on . We then say that is an isomorphism from

From your definition of (that is a set of the real ranks that satysfie for a fixed ) so we have that .

In other words we can define a function whit the property such that , at this point we have that the set of the is your

The question is, how do you know that is injective? It can be maybe a surjection on the reals (not-injective, multivalued)?

In fact from your definiton of seems me that you except it to be a countable subset of then you are asuming (is an hypothesis?) that is a bijection (is this what you mean when you say that they are isomorphic? And which is the funtion you use for the isomorphism? maybe you use ? )

Thanks in advance, and sorry for my bad english.

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