This online utility generates integers through Zermelo ordinals and prints a sequence of sets in the output. You can construct the full expansion of Zermelo ordinals using sets or abbreviated expansion using references to previous natural numbers. You can also specify the starting ordinal and the number of recursions. The ordinal output format can be customized as well by changing the set symbols. Created by math nerds from team Browserling.
This online utility generates integers through Zermelo ordinals and prints a sequence of sets in the output. You can construct the full expansion of Zermelo ordinals using sets or abbreviated expansion using references to previous natural numbers. You can also specify the starting ordinal and the number of recursions. The ordinal output format can be customized as well by changing the set symbols. Created by math nerds from team Browserling.
With this browser-based application, you can create a list of Zermelo ordinals, which are similar to the Von Neumann ordinals as you can find a bijection between both of them. The Zermelo ordinals are created by recursively adding the set of the preceding integer to a new empty set. There are two ways to write Zermelo ordinals. The first follows the recursive definition. It defines 0 to be the empty set ∅. Then, each next number n is constructed by wrapping the previous number n-1 in a set n = {n-1}. The first few levels of Ernst Zermelo's construction goes as follows: 0 = ∅, 1 = {∅}, 2 = {{∅}}, 3 = {{{∅}}}, …. The other way to write Zermelo ordinals is to use natural numbers as set elements. Zero is defined to be {} and each next number n is simply a set of the previous number {n-1}. The first few levels of this notation are as follows: 0 = {}, 1 = {0}, 2 = {1}, 3 = {2}, …. You can generate as many ordinals as you want by specifying the required number of output items in the options. It is not necessary to generate the sequence from the zeroth element and you can specify any starting integer. You can also customize the notation of Zermelo ordinals. In particular, you can specify the left set character (by default, it's an open curly bracket), the right set character (by default, it's a close curly bracket), and the empty set element (by default, it's a crossed zero ∅). Zermelabulous!
With this browser-based application, you can create a list of Zermelo ordinals, which are similar to the Von Neumann ordinals as you can find a bijection between both of them. The Zermelo ordinals are created by recursively adding the set of the preceding integer to a new empty set. There are two ways to write Zermelo ordinals. The first follows the recursive definition. It defines 0 to be the empty set ∅. Then, each next number n is constructed by wrapping the previous number n-1 in a set n = {n-1}. The first few levels of Ernst Zermelo's construction goes as follows: 0 = ∅, 1 = {∅}, 2 = {{∅}}, 3 = {{{∅}}}, …. The other way to write Zermelo ordinals is to use natural numbers as set elements. Zero is defined to be {} and each next number n is simply a set of the previous number {n-1}. The first few levels of this notation are as follows: 0 = {}, 1 = {0}, 2 = {1}, 3 = {2}, …. You can generate as many ordinals as you want by specifying the required number of output items in the options. It is not necessary to generate the sequence from the zeroth element and you can specify any starting integer. You can also customize the notation of Zermelo ordinals. In particular, you can specify the left set character (by default, it's an open curly bracket), the right set character (by default, it's a close curly bracket), and the empty set element (by default, it's a crossed zero ∅). Zermelabulous!
In this example, we construct Zermelo ordinals by wrapping the empty set in more sets. Each ordinal stage is generated by creating a set from the set at the previous stage. We output nine ordinals from zero to eight. Zero is ∅ and eight is ∅ in eight sets {{{{{{{{∅}}}}}}}}.
This example creates a sequence of Zermelo numbers via positive integers. Zero is defined to be {} and each next integer is the previous integer wrapped in a single set. So, zero is {}, one is {0}, two is {1}, and so on.
In this example, we change the set notation. We use square brackets instead of curly brackets to open and close a set. We also use the star symbol for the set with no elements. The generated ordinals start from the 3rd ordinal and six more are printed.
You can pass options to this tool using their codes as query arguments and it will automatically compute output. To get the code of an option, just hover over its icon. Here's how to type it in your browser's address bar. Click to try!
Create a drawing that visualizes von Neumann hierarchy of sets.
Create a sudoku puzzle.
Create a list of neat-looking integers (called magic integers).
Generate a list of tuples of integers with n elements.
Quickly convert integers to base one.
Quickly convert base one to integers.
Quickly convert integers to base two.
Quickly convert base two to integers.
Quickly convert integers to base eight.
Quickly convert base eight to integers.
Quickly convert integers to base sixteen.
Quickly convert base sixteen to integers.
Quickly encode integers to base-64.
Quickly decode base-64 to integers.
Quickly convert integers to a custom base.
Quickly encode integers to HTML encoding.
Quickly decode HTML entities to integers.
Quickly encode integers to URL (percent) encoding.
Quickly decode URL-encoded integers.
Quickly convert a signed integer to an unsigned integer.
Quickly convert an unsigned integer to a signed integer.
Generate a list of random integers.
Check if the given integers are palindromes.
Create a matrix whose entries are all integers.
Create a vector with integer coefficients.
Quickly calculate the average value of integers.
Quickly calculate the average value of integer digits.
Quickly randomly select a digit from an integer.
Find which of the given integers is the biggest or smallest.
Limit integer values to a range.
Limit integer digit values to a range.
Create multiple copies of the input integers.
Create multiple copies of digits of input integers.
Rotate the digits of an integer to the left or right.
Move the digits of an integer to the left or right.
Quickly find the difference of a bunch of integers.
Quickly apply the bitwise AND operation to integers.
Quickly apply the bitwise OR operation to integers.
Quickly apply the bitwise XOR operation to integers.
Quickly apply the bitwise NOT operation to integers.
Quickly apply the bitwise NAND operation to integers.
Quickly apply the bitwise NOR operation to integers.
Quickly apply the bitwise NXOR operation to integers.
Quickly divide two or more integers.
Quickly divide the digits of an integer.
Add -st, -nd, -rd, -th suffixes to integers to make them ordinals.
Remove -st, -nd, -rd, -th suffixes from ordinals to make them ints.
Find integers that match a filter (greater, less, equal).
Add padding to integers on the left side.
Add padding to integers on the right side.
Position all integers so that they align on the right.
Position all integers so that they align in the middle.
Turn all integers into positive integers.
Turn all integers into negative integers.
Rewrite an integer in fractional form.
Extract the numerator and denominator from a fraction.
Search for all occurrences of an integer and replace it.
Create a regex that matches the given integers.
Create integers that match the given regular expression.
Create relatively tiny integers.
Create relatively huge integers.
Create a sequence of oscillating integers, such as 123212321.
Create multiple integer sequences at once.
Slightly change an integer so it has an error.
Slightly change integer digits so there are errors.
Apply fuzzing to integers and add perturbations.
Apply fuzzing to integer digits and add digit perturbations.
Add highlighting to certain integers.
Add highlighting to certain integer digits.
Add color to integers based on a condition.
Add color to individual digits in the given integers.
Quickly assign colors to integers and draw them as pixels.
Quickly assign integer values to pixel colors and print them.
Make the digits of an integer go in a spiral shape.
Make the digits of an integer go in a circle.
Make the digits of an integer go in a diamond shape.
Fill a box with certain width and height with digits.
Use ASCII art to convert integers to 2-dimensional drawings.
Use ASCII art to convert integers to 3-dimensional drawings.
Decompose an integer into ones, tens, hundreds, etc.
Generate an ordered list of increasing integers.
Generate an ordered list of decreasing integers.
Quickly find various information about the given integers.
Find hidden patterns of numbers in integers.
Find the Shannon entropy of an integer.
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We're Browserling — a friendly and fun cross-browser testing company powered by alien technology. At Browserling our mission is to make people's lives easier, so we created this collection of integer tools. Our tools have the simplest user interface that doesn't require advanced computer skills and they are used by millions of people every month. Our integer tools are actually powered by our programming tools that we created over the last couple of years. Check them out!
