Question

Differentiate between a collection and a set.​

Answer 1

Answer:

Set guarantees that the collection will contain unique elements (no duplicates). A Collection does not guarantee this. The Set interface contains only methods inherited from Collection and adds the restriction that duplicate elements are prohibited. ... Two Set instances are equal if they contain the same elements.

Answer 2

Step-by-step explanation:

• Set theory, as initiated by Cantor, was thought of as a theory of collections. He “defined” a set as a whole of distinct objects, even if only from our formal thoughts. That is, the starting point was the analogy of sets with collections of things from our surroundings or imagination. But mathematics evolved. The abstract notion has emerged, and from a formal point of view, set theory speaks of nothings. We can developed a set theory without any mention of the word “set”. The very notion of the basic entity comes from the interpretation of the theory. But OK, let us imagine it intends to speak of sets. Are sets collections? Impossible to answer. The notion of set is given by the axioms we use. So, in ZFC set theory, supposed consistent, there is not an universal set, but it does exist in Quine-Rosser NF set theory. Sets are those things given by the axioms you use, and it results that the notion of set becomes relative to the theory being considered. Something may be a set in one theory, but not in others. “Collection” is, as far as I can imagine, an informal word for aggregate or amount of things, standard things like pebbles and cats, which of course can be represented by sets, but have nothing to do with abstract mathematics.