# Set Theory - Intersection, Union, Difference, Sort

A calculator for the set theory. Two sets of numbers or characters can be intersected, joined, subtracted and sorted. The elements will be counted and multiples will be deleted. Please enter any amount of values for Set A and Set B and choose whether the values are numbers or characters. At numbers, comma and point will be interpreted as decimal separator. As separators between the elements, space, break and semicolon can be used.

**Correct set x**: converts every element from set A or B into a number, sorts those and deletes multiples. The result will be written into the input field.

**Intersection**: and-operation, calculates the intersection of set A and B and corrects it. If an element was in set A and in set B before, then it will be in the result set.

**Union**: -operation-operation, calculates the joining of set A and B and corrects it. If an element was in set A or in set B or in both before, then it will be in the result set.

**Difference x-y**: takes all the elements from one set and removes those that also occur in the other set.

**XOR**: exclusive or, takes only those values which are in one set, but not in both.

**Example**: presets some simple values for set A and B. With those, the calculation operations can be performed.

Sets are summaries of objects. These objects may or may not be numbers. A well-known and frequently used set is that of the natural numbers ℕ. Set theory was founded by Georg Cantor at the end of the 19th century. It is an important branch of mathematics and provides some of the foundations for its formulation. Naive set theory is unrestricted, but contains contradictions, including *Russell's antinomy* with the *class of all classes that do not contain themselves as an element*. Bertrand Russell's solution was the restriction that a class must have a higher type than its elements.

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