Product Groups Part 2

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  • เผยแพร่เมื่อ 4 ม.ค. 2025

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  • @ANDROIDPOSTMORTEM
    @ANDROIDPOSTMORTEM 2 ปีที่แล้ว

    I think there is a better way to look at the mapping...
    For each element of the product group is similar to Cartesian coordinate then we cn easily think of the mapping as one from points over one 2d plane to itself... A bijective mapping

  • @leandrocarg
    @leandrocarg 5 ปีที่แล้ว

    Great!! One question: Shouldn't your underlaying set on wich you are defining GxG' to perform set permutations be SGxSG' (cartesian product) instead of SGUSG'?
    I mean, it's ok if SG and SG' are distinct, but what if SG=SG' or the intersection is non-empty? Your set permutations will no longer be bijective because of the degeneracy of the union, in fact it will no longer be injective (you'll have more permutations than elements).
    So, even if your sets are exactly equal, the cartesian product takes cares of the whole situation, because your product group and the cartesian product have now the exact same number of elements. Great Series BTW, this is the second time I watch it and it is absolutely exelent!

  • @tabmax22
    @tabmax22 5 ปีที่แล้ว +1

    blue and turquoise looks the exact same