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January 4th, 2015, 11:37 PM   #1
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How I can define an equivalence relation on the graph of a function?

Let $a∈ℝ$ being fixed. Let $g:ℝ→ℝ$ be a real analytic function with infinitely many zeros.

I want to classify the points $c,d$ such that $g(a)=(a-u)g′(c)≠0$ and $g(a)=(a-w)g′(d)≠0$ where $c∈(u,a)$ and $d∈(w,a)$ with $g(u)=g(w)=0$ and $u≠w,a≠u,a≠w$.

I am thinking about an equivalence relation. However, I am not able to formulate it mathematically.
Ganesh Ujwal is offline  

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