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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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Yes. bitwise-or of the modulo(remainder). It is only zero if both modulos are zero.
When using it on bools you have to be a bit careful, as (1 | 2) is 0011, and that is stored in boolean. true is 0001, so while (1 | 2) evalutes to true, it's not equal to true in some way. Here it's fine, but be aware. Negating with ! (boolean not) "normalizes" it to 0000 or 0001 though. ~ would be the bitwise not.
bitwise-or may be faster as it does not branch (both sides are always evaluated), as opposed to boolean or. But don't rely on that.