Reading the description, your explanation of why the rationals are not a binary operation under division was unintentionally a bit funny. Because you say “you can’t divide by 0!” Well you can divide by 0!, since it is 1 😆
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the problem shouldn't be solved by giving the blank a variable at the level of an average 9 year old's ability. it's pretty simple. the bottom row 7, star, and 9 can get 40 by adding 7 + star + star + 9 to get 40. 7 + 9 = 16, so 2 * star = 24. this makes star 12, so 12 + 9 = 21. adding 12 and 21 gives us 33. no additional variables needed. i'm assuming that's how the problem was designed to be solved.
At 8:48 are you saying that the first example (0,2) : {(1/k, 2-1/k)} will not have a finite subcover because if we restrict the indexing set of k from 1 to infinity then it will always be impossible for that set to be able to cover (0,2). If other words k must go from 0 to infinity for {(1/k, 2-1/k)} to cover (0,2)? Is that line of thinking correct? Many thanks for all the Real Analysis videos, you have been a great help with my degree 😄
I would rather use a book that explains stuff, and not just throws a bunch of formulas on a page 1. The "big problem" is that modern book has more background information and easier to understand? Wow, so bad I guess.