projection m_s are +1/2 and -1/2, it follows that one electron must have m_s = +1/2 and one m_s = -1/2.

Particles with an integer spin (bosons) are not subject to the Pauli exclusion principle. Any number of identical bosons can occupy the same quantum state, such as photons produced by a laser, or atoms found in a Bose-Einstein condensate.

A rigorous statement which justifies the exclusion

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