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I have a function of the form S=f(x,y,z), 0 ≤ x ≤ 1,0 ≤ y ≤ 1, 0 ≤ z ≤ 1. I would like to solve S=0 numerically and plot the solution set of (x,y,z) in 3-space

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There is ContourPlot3D[] for this:

ContourPlot3D[x^2 + y^2 + z^2 == 1, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}]