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 Number theory and hyper operators MphLee Fellow Posts: 95 Threads: 7 Joined: May 2013 05/27/2013, 01:18 PM (This post was last modified: 05/27/2013, 03:36 PM by MphLee.) (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: $\mathbb{I}_{y} = \{ s_0 | s_0 \in \mathbb{R}\,\,;\,\,x\,\,\bigtriangleup_{s_0}\,\,y\,\,\in \mathbb{N}}$ claim that there are operators unique to x and y which allow us to perform operations on elements of $\mathbb{I}_y$ instead of operations on $\mathbb{N}$. We then say that $n\,\,\bigtriangleup_{s_n}\,\,y$ is an isomorphism from $\mathbb{I}_y \to \mathbb{N}$Sorry if my question is stupid (I'm a newbie in math) but I'm a bit confused. From your definition of $\mathbb{I}_{y}$ (that is a set of the real ranks $s_0$ that satysfie $\,\,x\,\,\bigtriangleup_{s_0}\,\,y\,\,\in \mathbb{N}$ for a fixed $y$ ) so we have that $\mathbb{I}_{y}\subset \mathbb R$. In other words we can define a function $I_y:\mathbb {N} \rightarrow R$ whit the property $I_y(n)=s_n$ such that $n\,\,\bigtriangleup_{s_n}\,\,y\in \mathbb{N}$, at this point we have that the set of the $s_0, s_1, s_3, ...$ is your $\mathbb{I}_{y}$ The question is, how do you know that $I_y:\mathbb {N} \rightarrow R$ is injective? It can be maybe a surjection on the reals (not-injective, multivalued)? In fact from your definiton of $\mathbb{I}_{y}$ seems me that you except it to be a countable subset of $\mathbb{R}$ then you are asuming (is an hypothesis?) that $I_y:\mathbb {N} \rightarrow \mathbb{I}_{y}$ 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 $I^{\circ -1}_y:\mathbb{I}_{y} \rightarrow \mathbb {N}$ ? ) Thanks in advance, and sorry for my bad english. MathStackExchange account:MphLee « Next Oldest | Next Newest »

 Messages In This Thread Number theory and hyper operators - by JmsNxn - 08/30/2012, 02:49 AM RE: Number theory and hyper operators - by tommy1729 - 08/30/2012, 01:45 PM RE: Number theory and hyper operators - by JmsNxn - 08/30/2012, 05:24 PM RE: Number theory and hyper operators - by MphLee - 05/27/2013, 01:18 PM RE: Number theory and hyper operators - by MphLee - 05/25/2013, 10:15 PM RE: Number theory and hyper operators - by JmsNxn - 05/27/2013, 11:33 PM RE: Number theory and hyper operators - by MphLee - 05/28/2013, 10:40 AM RE: Number theory and hyper operators - by MphLee - 05/29/2013, 09:24 PM

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