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 January 4th, 2015, 11:37 PM #1 Senior Member   Joined: Aug 2014 From: India Posts: 363 Thanks: 1 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.

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