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Collections are a way for you to organize kata so that you can create your own training routines. Every collection you create is public and automatically sharable with other warriors. After you have added a few kata to a collection you and others can train on the kata contained within the collection.
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You are ignoring the overlapse. For example the ex.1 Has 1-5 and 1-5. if you were to write every number between the both of them you would indeed get 9 numbers(length 8), but all of them would be dublicated. So the number of the unique numbers is 5(and the length is 4): 1, 2, 3, 4, 5; it is simpler to understand if you write the intervals on one line in a pice of paper. :)
We can forget about 1-5 and 16-19 because they are inside 1-6 an 10-20. 1-6 and 5-11 = 1-11. And 1-11 and 10-20 = 1-20. It's length = 20-1 = 19;