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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 $g(a)=(au)g′(c)≠0$ and $g(a)=(aw)g′(d)≠0$ 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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define, equivalence, function, graph, relation 
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