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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.
Get started now by creating a new collection.
0 is a debated natural number and can be a member of the natural number set depending on which set you are using. See here http://oeis.org/A000027.
However, I agree with you on the fact it should state that it is including 0 as a natural number.