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**1. The problem statement, all variables and given/known data**prove , using appropriate commutation relations that the number operator yields the values 0 and 1 for fermions , and any non - negative values for bosons.

**2. Relevant equations**the commutation relations for bosons and fermions.

**3. The attempt at a solution**the boson case is solved.

the fermions-i can understand this thing intuitively ,because on applying the number operator on a state containing n fermions in a single state , and then using commutation relation i am getting (-n) as eigenvalue which is absurd. but i do not know how to give a more compact proof.