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In my work I am dealing with an equation that will have 1 or more solutions. Specifically I am trying to find local maximums. I am not interested in the solutions to the equation, but I am instead interested in how many solutions there are. Is there any way to formally state this? I was thinking that I would define the solutions to the equation to form a set and then the answer to my problem would simply be the cardinality of that set. Is this the way to state it or is there more concise notation for this?

mjnichol
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    then show us your equation please – Dr. Sonnhard Graubner Jan 05 '15 at 20:31
  • The specific equation is not really relevant. I am just wondering how to formally state the number of solutions an equation has. – mjnichol Jan 05 '15 at 20:44
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    We would need to see your equation to give a concrete answer, but the solutions may not strictly be a set since (at least in polynomials), one solution could have a higher multiplicity. Consider $x^2(x-1)=0$. It has a solution of 0 twice and 1 once. – Jemmy Jan 05 '15 at 22:17
  • Ah, I see. In my case I am attempting to determine the number of local maximums of a transcendental equation. I imagine that if there were any solutions with a higher multiplicity I would not want to double count them since I would not truly have more maximums. In this case I think the set cardinality is the way to go. Thanks for helping me explore the idea! – mjnichol Jan 05 '15 at 23:49

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