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The dipole is the fundamental elemental antenna, and the wire electric dipole and its monopole equivalent are still widely used in practice. Despite the long history of dipole research, its complete impedance behavior remains elusive, because of long-standing shortfalls in modeling the feed. The available analytic approaches are the wave-structure method and the induced-EMF method. The wave-structure method does not lend itself to feed-gap detail. However, it reveals the impact of the dipole's thickness and length on the impedance of dipoles, which is not readily available from other approaches. The method is restricted to an infinitesimal feed gap, i.e., different from a practical dipole antenna. The induced-EMF method is accurate for short and impracticably thin (for self-supporting) wire antennas. Numerical techniques can be used for practical dipole thicknesses, but no theory is available to benchmark the results. Here, the induced-EMF method with a finite feed gap is solved, and the impedance of the thin dipole is presented. The bandwidth is the critical parameter, and other methods are also applied for calculating the theoretical bandwidth. It is of particular interest that the lossless, thin dipole with a finite gap is a structure that has an extremely wide bandwidth. This paper includes a brief review of previous work to acknowledge the rich history and provide context for current research. However, it mostly presents new analysis and new impedance-bandwidth results for a range of dipole lengths.