Fermat's Last Theorem … (GN_+)

This paper introduces a geometric and set-theoretic framework, titled "Taha’s Geometry Shapes & \(\mathbb{N}_{+}\) Fact," to evaluate Fermat's Last Theorem (\(a^n + b^n = c^n\) for \(n > 2\)). We partition the infinite set of positive integers \(\mathbb{N}_{+}\) into five distinct geometric and structural subsets based on the triangle inequality theorem and segment relations: Right Triangles (\(S_{1}\)), Acute Triangles (\(S_{2}\)), Obtuse Triangles (\(S_{3}\)), Perfect Segments where \(a+b=c\) (\(S_{4}\)), and Degenerate Segments where \(a+b 2\).