What is the opposite of a set? скачать в хорошем качестве

What is the opposite of a set?

The "opposite" of being finite is having a finite complement. The "opposite" of a vector is a linear functional. If a set is a small collection of elements... then what is the "opposite" of a set? __________ Errata: 2:53 - Some of the equations are incorrect; thanks ‪@sstadnicki‬! 6:18 - The preimage function g^{-1} is pointing the wrong way; it should be mapping P(X) to P(Y)... like every other instance of g^{-1} in this video. Thanks ‪@ДмитрийГнатюк-к4ц‬ ! 14:23 - This example is not complete! The algebra here does not have infinite joins... sorry everyone! This only provides an example of a Boolean algebra with no atoms. For a complete Boolean algebra with no atoms, you can take a similar-looking (but much bigger example) of Lebesgue measurable subsets of the real numbers, where two subsets are viewed as "essentially the same" if they differ by a set of Lebesgue measure zero. Thank you @SlipperyTeeth for pointing out the error with the infinite joins and meets, and thank you also to @yuvalpaz3752 for demonstrating that A doesn't have infinite joins at all. __________ Timestamps: 00:00 - Introduction 01:18 - Cosets, as the name implies 02:02 - Formal duality 03:51 - Undoing functions 04:53 - Preimage 06:30 - Towards an algebraic definition of cosets 08:22 - The structure of a coset 09:35 - Function reconstruction 12:41 - Cosets are a kind of algebra 13:22 - John Dalton would be very upset with this example 15:55 - Coset building blocks 16:40 - Thx 4 watching!