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January 22nd, 2013, 05:31 AM  #1 
Newbie Joined: Aug 2012 Posts: 8 Thanks: 0  Is this proof valid
Let: x,u,y,v:C?R be functions in the complex variable s=a+ib defined by convergente series. I have this implication: If x(s)=u(s),y(s)=v(s) , then after some steps on these series one get an equation of the form: h(s)=0 which give one value of s as s=1+ib for some b . I call this result (s=1+ib ) as "(P)". The function h here depends on the given functions x,u,y,v . Its formula is not important. let A=s?C(s)=u(s),y(s)=v(s) and B=s?C(s)=u(s)=y(s)=v(s)=0 is a proper subset of A . I know that if s?A then (P) holds true. My question is as follow: What happen if s?B . Is (P) true or false!. We remark here that if s?B then we cannot construct the function h and hence we cannot deduce (P), i.e., if x(s)=u(s)=y(s)=v(s)=0 then I cannot do anything and the proof stoped here. 
January 22nd, 2013, 01:51 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,856 Thanks: 745  Re: Is this proof valid
I'll start by saying I have no idea what you are trying to do. However you say that something is true for (all?) s in A. Since B is a subset of A, it will be true for s in B. 
January 28th, 2013, 03:37 AM  #3 
Senior Member Joined: Dec 2012 Posts: 148 Thanks: 0  Re: Is this proof valid
could you post original version of problem???


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