Precision results on cosmic-ray electrons are presented in the energy range from 0.5 GeV to 1.4 TeV based on 28.1×106 electrons collected by the Alpha Magnetic Spectrometer on the International Space Station. In the entire energy range the electron and positron spectra have distinctly different magnitudes and energy dependences. The electron flux exhibits a significant excess starting from 42.1+5.4−5.2  GeV compared to the lower energy trends, but the nature of this excess is different from the positron flux excess above 25.2±1.8  GeV. Contrary to the positron flux, which has an exponential energy cutoff of 810+310−180  GeV, at the 5σ level the electron flux does not have an energy cutoff below 1.9 TeV. In the entire energy range the electron flux is well described by the sum of two power law components. The different behavior of the cosmic-ray electrons and positrons measured by the Alpha Magnetic Spectrometer is clear evidence that most high energy electrons originate from different sources than high energy positrons.