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First you must understand the term of disjoint sets. This is when both sets have no elements in common.
Ex: A={2,3,4} B={1,5,9}. Since A has no similar numbers in B and likewise, they are disjoint.
A is a partition of a finite or infinite collection of nonempty sets G= {A,B,C,D...},Iff:
1) A is in the union of all {A,B,C,D...}
2) The sets A,B,C,D...are all mutually disjoint (no overlapping of elements)
So in other words, A=/B=/C=/D=/... ---(=/ is 'does not equal')---
i.e. (A intersect B) = {} ---- ({} is an empty set)---
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Discrete Mathematics is mathematics that deals with discrete objects and operations, often using computable and/or iterative methods. It is usually opposed to continuous mathematics (e.g. classical calculus). Discreteness here refers to a property of subjects of discourse. Some collection of things is called discrete if these things are distinguishable and not continuously transformable into each other. An example would be the collection of natural numbers, but not the real numbers. In topology, a space is called discrete if every subset is open. In constructivism, a set is called discrete if equality of two elements is always decidable.
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