Applications and differences for Jaccard similarity and Cosine Similarity Jaccard similarity and cosine similarity are two very common measurements while comparing item similarities. However, I am not very clear in what situation which one should be preferable than another.

Can somebody help clarify the differences of these two measurements (the difference in concept or principle, not the definition or computation) and their preferable applications?
The answer from saq7 is wrong, as well as not answering the question.

∥A∥ means the $L2$ norm of $A$, i.e. the length of the vector in Euclidean
space, not the dimensionality of the vector $A$.  In other words, you
don't count the 0 bits, you add up only the 1 bits and take the square root.

Sorry I don't have a real answer as to when you should use which metric,
but I can't let the incorrect answer go unchallenged.