query: If $f^3=\rm id$ then it is identity function
positive_passages.docid: 16338
positive_passages.text: 3rd iterate of a continuous function equals identity function
negative_passages.docid: 145879
negative_passages.text: $R$ is PID, so $R/I$ is PID, and application on $\mathbb{Z}$ and $\mathbb{N}$
negative_passages.docid: 44100
negative_passages.text: Prove that identity element is unique
negative_passages.docid: 146152
negative_passages.text: Characterising functions $f$ that can be written as $f = g \circ g$?
negative_passages.docid: 52354
negative_passages.text: Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
negative_passages.docid: 46875
negative_passages.text: The identity morphism in $\mathbf{Set}$ is the identity function
negative_passages.docid: 123044
negative_passages.text: Commutative matrices are multiples of the identity
negative_passages.docid: 76510
negative_passages.text: vector identity for triple scalar product
negative_passages.docid: 106894
negative_passages.text: If a subring of a ring R has identity, does R also have the identity?
negative_passages.docid: 28925
negative_passages.text: Can the Identity Map be a repeated composition one other function?
negative_passages.docid: 19355
negative_passages.text: prove $f(x)=x^3+x$ is one to one and onto
negative_passages.docid: 140140
negative_passages.text: An identity which applies to all of the natural numbers
negative_passages.docid: 130620
negative_passages.text: Identity type between A and B being non-empty implies non-emptiness of A and B?
negative_passages.docid: 28927
negative_passages.text: IMO 1987 - function such that $f(f(n))=n+1987$
negative_passages.docid: 147659
negative_passages.text: Counterexample to "if $f:A\to A$ induces the identity $\hat f:\operatorname{Spec}(A)\to\operatorname{Spec}(A)$, then $f=\operatorname{id}_A$"
negative_passages.docid: 137422
negative_passages.text: $\mathrm{card}(\mathbb{Z}^n/M\mathbb{Z}^n) = |\det(M)|$?
negative_passages.docid: 46825
negative_passages.text: The identity det(A) = exp(Tr(ln(A)) for A general