Set Cardinality Calculator

This browser-based program finds the cardinality of the given finite set. For any given set, the cardinality is defined as the number of elements in it. For example, if the set A is {0, 1, 2}, then its cardinality is 3, and the set B = {a, b, c, d} has a cardinality of 4. The set's size is denoted by the vertical bar characters, for example, |A| = 3 and |B| = 4. If you know the cardinality of sets, then you can compare them by size and determine which set is bigger. If the cardinality of two sets is the same, then there is a bijection between them. The input set can be specified in the standard set format, using curly brace characters { } on the sides and a comma as the element separator (for example {1, 2, 3}) and in a non-standard set format (for example [1 2 3] or <1*2*3>). To customize the input style of your set, use the input set style options. You can change the element separator and the open-set and close-set characters. If the input set is a multiset (a set that allows including the same element several times), then two additional cardinality counting modes can be useful to you. The "Count Only Unique Elements" mode counts each item only once. If any of the elements in the set are duplicated, then their copies are not included in the count. For example, the cardinality of the set A = {a, a, b} in this counting mode is 2 because "a" is a repeated element. The other cardinality counting mode "Count Only Duplicate Elements" does the opposite and counts only copies of elements. In this case, the set A = {a, a, b} has the cardinality of 1 because the element "a" is the only element that is repeated. All counting modes are connected via the relation "total elements = unique elements + repeated elements". The last checkbox "Include Empty Elements" can be very helpful in situations when the set contains empty elements. With this option, you can either include or exclude empty elements from the count. Setabulous!