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Base Change Conversions
Converts a positive integer to Binary-Octal-Hexadecimal Notation or Binary-Octal-Hexadecimal Notation to a positive integer. Also converts any positive integer in base 10 to another positive integer base (Change Base Rule or Base Change Rule or Base Conversion)

Complex Number Operations
Given two numbers in complex number notation, this calculator:
1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.
2) Determines the Square Root of a complex number denoted as √a + bi
3) Absolute Value of a Complex Number |a + bi|
4) Conjugate of a complex number a + bi

Expanded Notation
Writes the expanded notation for a number.

Interval Notation and Set Builder Notation
This calculator translates the following inequality statements to interval notation and set builder notation:
* x < 5
* y <= 5
* z > 5
* a >= 5
* b < 5 or b > 20
* Compound Inequality such as 0 <= c < 4
* |x|<3
* Reverse Interval Notation to Inequality Statement such as (-7,5]
* {x|x<1}
* Word representations of interval notations such as 2 is less than or equal to x is less than or equal to 8

Lagrange Four Square Theorem (Bachet Conjecture)
Builds the Lagrange Theorem Notation (Bachet Conjecture) for any natural number using the Sum of four squares.

Plane Geometry Operations
Lists detail and simplifies various plane geometry operations and notations

Plane Geometry Operations
Evaluates and simplifies various plane geometry notation and operations

Roster Notation
Given a set of numbers, this displays the roster notation

ROT-13 Conversions
This calculator converts ROT-13 (rot13) (rotate by 13 places) notation to standard notation or standard notation to ROT-13 notation.

Scientific Notation
* Converts a number into scientific notation and determines order of magnitude
* converts scientific notation to a number (standard notation). Also handles scientific notation operations.

Set Notation
Given two number sets A and B, this determines the following:
* Union of A and B, denoted A U B
* Intersection of A and B, denoted A ∩ B
* Elements in A not in B, denoted A - B
* Elements in B not in A, denoted B - A
* Symmetric Difference A Δ B
* The Concatenation A · B
* The Cartesian Product A x B
* Cardinality of A = |A|
* Cardinality of B = |B|
* Jaccard Index J(A,B)
* Jaccard Distance Jσ(A,B)
* Dice's Coefficient
* If A is a subset of B
* If B is a subset of A

Set Theory Notation
Evaluates and describes various set theory notation

Standard Notation
Calculates the following:
* The numeric notation of word notation
* Standard notation of expanded notation

Standard Notation
Displays the Standard notation of expanded notation

Word Notation
Calculates the following:
* The word notation of a number of numeric expression

X is a natural number greater than 6
One and one third less x
The sum of 5x and 2x is at least 70
Nine less than the product of 2 and y is not less than 15
-3x<= -9 or 5+x<6
the sum of a number times 3 and 30 is less than 17
-2 <= x +4 < 9
x is smaller than 9 and greater than 4
The product of x and 7 is not greater than 21