302.3A: Review Of Homomorphisms
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Jordan Regan: What do you mean by 'On-to' (a qualification for Isomorphism)? I started watching your videos with Group Theory, so may have missed the part explaining this. Could you direct me to a learning platform for this or explain it quickly as a Google search of 'On-to Morphism' returns no worthwhile results? Thx TARINunit9: 1:10 Thank you so damn much Bon Bon: Are those morphisms the same as in category theory? Because they sound oddly familiar :q Ravish Kumar: Your illustration is so good sir....... Mani Megalai: very useful mathIsART: In order for a map between groups to be an isomorphism, why is it not necessary to prove that its inverse is a homomorphism, too? Why is it only necessary to prove that it is a bijective homomorphism? The same reasoning does not apply to continuous functions between topological spaces (where we must prove that the inverse is continuous too) or holomorphic functions on the complex plane (where we must prove that the inverse is holomorphic too). Hythloday71: What is the character of the structure that is preserved by homomorphisms generally ? Could it be said that an 'isomorphism' preserves 'information' in the physics sense of preserving distinctions ? Or is that what is generally done with homomorphisms ? Thinking about it, the particular cases of onto and 1-1 just serving to inform about the complete structure accountability ? There seems also something perhaps 'order' preserving about a homomorphism ? amit parte: nice explanation Romario Tambunan: thanks you so much!!!! this is the best explanation Mahammad Rustamzade: Angel :D Thanks, you saved my life :D M Mahboob Khan Raja: Lot of thanks i got it Jordi Grau: Many thanks. I love your videos. I feel very confortable learning with you about a subject that I am very interested in. sanjursan: Good Vid!! More fun to watch Liliana de Castro, but more and better info here. Thank you for this vid. OuafiEddine Naciri: Hi Anthony If we choose 2^n it works, I mean we obtain an homomorphism. All that we lose is : that is neither a monomorphism nor an epimophism. Hanz Albert Nguyen: you are doing good presentation, but you are talking as if you are robbing, slow downnnnnnn , mannn! Debendra Bhue: show that the group l 1 a l such that a €z is iso morphic to Z Anthony Casadonte: For the automorphism example, saying how phi is its own inverse makes me think of whether we can have a group of homomorphisms with the binary operation of composition. The identity is the trivial homomorphism and in this case the inverses are themselves. Can we think of this? Anthony Casadonte: I see how the function you chose "3^n" works between addition and multiplication operations given the rules of exponents, so that is one way to get an intuitive sense of why you chose that particular function as the homomorphism. But, why in particular the base 3? I see how it would not work with 2, but would it work with 5? In general, for a group of integers with addition and the multiplicative group of integers for another modulus, I see why exponentiation makes sense but what about the base? |
302.3A: Review of Homomorphisms
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