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visits member for 3 years, 11 months
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Jan
6
comment Fundamental group of projective plane is $C_{2}$???
Related: An intuitive idea about fundamental group of $\mathbb{RP}^2$
Jan
6
revised Fundamental group of projective plane is $C_{2}$???
edited tags
Jan
6
reviewed Close $C$ Hermitian, show $\text{Tr}(C)=0 \iff \exists P,Q \text{ Hermitian s.t.} \,\, PQ-QP=iC$
Jan
6
reviewed Close Eigenvalues and eigenvectors of AB and BA in Endomorphisms
Jan
6
comment What are some examples of hard theorems in category theory?
(In the title you're asking about deep theorems but the body asks for difficult proofs — maybe that's why that quote came to my mind.)
Jan
6
comment What are some examples of hard theorems in category theory?
In Récoltes et Semailles Grothendieck described two styles in mathematics. One: «put the cutting edge of the chisel against the shell and strike hard. If needed, begin again at many different points until the shell cracks»; and another: «The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it… yet it finally surrounds the resistant substance» (translation by C. McLarty, AFAIK).
Jan
6
revised Question about a nested radical identity of Ramanujan involving $\sqrt 5$
edited tags
Jan
6
revised Infinite radical. How to show it converges to three?
edited tags
Jan
6
revised How to prove $\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$
edited tags
Jan
6
reviewed Close characteristic polynomial of companion matrix
Jan
6
reviewed Close Adding members of the Cantor set to get $[0,2]$
Jan
6
revised $\operatorname{Hom}(f^*F, G) = \operatorname{Hom}(F, f_*G)$
tex in title
Jan
6
reviewed Looks OK Let $G = \{1, a, b, c\}$ be a group of order 4…Exist two groups of order $4$.
Jan
6
reviewed Looks OK Way to determine eigenvalues from 3. degree characteristic equation?
Jan
6
revised How to prove that $\sum_{i=0}^{a}\frac{i\binom{a+b-c-i}{a-i}\binom{c+i-1}{i}}{\binom{a+b-1}{a}}=\frac{ac(a+b)}{b(b+1)}$
formatting, tags
Jan
6
reviewed Close What is $Spec(\mathbb{Z}[x])$?
Jan
5
revised Finite subgroups of SO(3) are defined by ramified coverings of Riemann spheres
minor tex/formatting
Jan
5
reviewed Close Proving divergence of $\sum_2^\infty{(-1)^n}{1\over \sqrt n+(-1)^n}$
Jan
5
comment How do I prove that $\binom{n}{k} \cdot k=n \cdot \small\binom{n-1}{k-1}$
See also «intuitive explanation»
Jan
5
comment How do I prove that $\binom{n}{k} \cdot k=n \cdot \small\binom{n-1}{k-1}$
Duplicate of: Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$ (not speaking of Wikipedia etc)