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The definition that I have concluded is that:

No two fermions can exist in the state, or quantum state, unless they have opposite spins. Am I right in saying this? They can have the same azimuthal number, the same principle quantum number, and thus the same magnetic number but if they have a different spin it's alright?

Any clarification appreciated. Thanks!

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The Pauli exclusion principle is - "No two fermions can occupy same quantum state." i.e. If two electrons have same principal, azimuthal and magnetic no. then they must have different spin quantum number.

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The answer is yes - if they do have the same azimuthal number, the same principle quantum number, and thus the same magnetic number but if they have a different spin it's alright. See link below for more help: LINK

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