cong for dogs - Pets Zone
MSN: Cong MP brings dog to Parliament, says 'those who bite are in govt' The Congress found itself in a rather unusual controversy after its Rajya Sabha MP Renuka Chowdhury arrived in Parliament with a dog on Monday. However what sparked an outrage was her analogy between ... Cong MP brings dog to Parliament, says 'those who bite are in govt' In geometry, $\cong$ means congruence of figures, which means the figures have the same shape and size.
Understanding the Context
(In advanced geometry, it means one is the image of the other under a mapping known as an "isometry", which provides a formal definition of what "same shape and size" means) Two congruent triangles look exactly the same, but they are not the ... I went through several pages on the web, each of which asserts that $\operatorname {Aut} A_n \cong \operatorname {Aut} S_n \; (n\geq 4)$ or an equivalent statement without proof, and many of them seem to regard it as a trivial fact. The proof given for the theorem is the following: "The description of line bundles in terms of their cocycles provides us with an isomorphism $\operatorname {Pic} (X) \cong \check {H^1} (X,\mathcal {O}^*_X) $ ". Proving the isomorphism $Pic (X) \cong H^1 (X,\mathcal {O}^*_X) $ in ...
Image Gallery
Key Insights
Prove that $\mathbb Z_ {m}\times\mathbb Z_ {n} \cong \mathbb Z_ {mn}$ implies $\gcd (m,n)=1$. This is the converse of the Chinese remainder theorem in abstract algebra.