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Set cardinality calculator

World's simplest set tool

With this online application, you can quickly find the cardinality of the given set. The input set can be written in any notation and you can adjust its style in the options. You can also use several different cardinality calculation modes to find the size of regular sets (with non-repeated elements) and multisets (with repeated elements). You can also exclude empty elements from the count. Created by team Browserling.
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Input Set Style
The element separator symbol that goes between elements.
Open set symbol.
Close set symbol.
Cardinality Counting Mode
Count all elements in the input set.
If the input set is a multiset then count only the unique elements in it.
If the input set is a multiset then count only the duplicate elements in it.
Element Options
If the set contains blank elements, then include them in the count.
Set cardinality calculator tool What is a 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!
Set cardinality calculator examples Click to use
Cardinality of a Set of Primes
In this example, we paste a set of primes less than 100 in the input box and we want to find how many primes there are in this interval. The entered set uses the standard set style, namely comma-separated elements wrapped in curly brackets, so we use the comma as the number separator and braces { } as set-open and set-close symbols. We select the mode that counts all the elements in the set and find that the cardinality of this set is 25, which means there are 25 primes less than 100.
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}
25
Required options
These options will be used automatically if you select this example.
The element separator symbol that goes between elements.
Open set symbol.
Close set symbol.
Count all elements in the input set.
If the set contains blank elements, then include them in the count.
Size of a Set of Equations
The input set in this example is a collection of simple math expressions in variables x and y. If you look closely, you can see that some of the expressions are duplicated, which means that the input set is a multiset. To avoid counting repeated expressions, we activate the "Count Unique Elements" option. Also, to adapt the program to the non-standard set format that uses square brackets and semicolons, we put a semicolon in the set element delimiter field and square brackets in the fields for left and right set symbols.
[x; y; x + y; x + 1; y + 1; 2x; 2y; 2x + 1; 2y + 1; x²; y²; x² + 1; y² + 1; x² + x; y² + y; x² + x + 1; y² + y + 1; x; y + 1; 2y; x² + 1; y² + y; x² + x + 1]
17
Required options
These options will be used automatically if you select this example.
The element separator symbol that goes between elements.
Open set symbol.
Close set symbol.
If the input set is a multiset then count only the unique elements in it.
If the set contains blank elements, then include them in the count.
Unicode Checkmarks Set
In this example, the elements of the set are Unicode checkmarks that are separated by dashes. Each set element occurs at least two times and there are many empty elements in the set (between two dashes). We exclude the blank items from the count by turning off the empty element checkbox option. By using the "Count Repeated Elements" mode, we find the number of duplicate checkmarks in the set, which is 12.
✓-✅-✕- -☑-✅-✘--✔-✖-✔-✅-✘-☑--❌-✔-✗--✅-✗-✓- -✖-❌-✘
12
Required options
These options will be used automatically if you select this example.
The element separator symbol that goes between elements.
Open set symbol.
Close set symbol.
If the input set is a multiset then count only the duplicate elements in it.
If the set contains blank elements, then include them in the count.
Pro tips Master online set tools
You can pass input to this tool via ?input query argument and it will automatically compute output. Here's how to type it in your browser's address bar. Click to try!
https://onlinesettools.com/find-set-cardinality?input=%7B2%2C%203%2C%205%2C%207%2C%2011%2C%2013%2C%2017%2C%2019%2C%2023%2C%2029%2C%2031%2C%2037%2C%2041%2C%2043%2C%2047%2C%2053%2C%2059%2C%2061%2C%2067%2C%2071%2C%2073%2C%2079%2C%2083%2C%2089%2C%2097%7D&input-separator=%2C%20&input-open-set=%7B&input-close-set=%7D&count-all=true&count-empty=true
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Delete all duplicate elements from a set (leave unique).
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Find all unique elements in a set.
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Delete all unique elements from a set (leave duplicates).
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Pick a random subset of the given set.
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Create a set with no elements.
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Create a set that contains digits.
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Create a set that contains numbers.
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Create a set that contains integers.
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Create a set that contains decimal fractions.
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Create a set that contains letters.
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Create a set that contains characters.
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Create a set that contains words.
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Create a set that contains strings.
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Create a set that contains text.
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Create a set that contains sentences.
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Create a set with infinitely many elements.
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Change the open-set, close-set, and element separator symbols.
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Add or remove set elements to make it a certain size/length.
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Analyze a set and print its statistics.