Search results
Results from the WOW.Com Content Network
The order of operations, that is, the order in which the operations in an expression are usually performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages. It is summarized as: [2] [5] Parentheses; Exponentiation; Multiplication and division; Addition and subtraction
It follows from the preceding equations that = when x is an integer (this results from the repeated-multiplication definition of the exponentiation). If x is real, = results from the definitions given in preceding sections, by using the exponential identity if x is rational, and the continuity of the exponential function otherwise.
The first three values of the expression x[5]2. The value of 3[5]2 is 7 625 597 484 987; values for higher x, such as 4[5]2, which is about 2.361 × 10 8.072 × 10 153 are much too large to appear on the graph. In mathematics, pentation (or hyper-5) is the fifth hyperoperation.
The sequence starts with a unary operation (the successor function with n = 0), and continues with the binary operations of addition (n = 1), multiplication (n = 2), exponentiation (n = 3), tetration (n = 4), pentation (n = 5), etc. Various notations have been used to represent hyperoperations.
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Help; Learn to edit; Community portal; Recent changes; Upload file
In mathematics, the exponential function can be characterized in many ways. This article presents some common characterizations, discusses why each makes sense, and proves that they are all equivalent. The exponential function occurs naturally in many branches of mathematics. Walter Rudin called it "the most important function in mathematics". [1]
For example, when computing x 2 k −1, the binary method requires k−1 multiplications and k−1 squarings. However, one could perform k squarings to get x 2 k and then multiply by x −1 to obtain x 2 k −1. To this end we define the signed-digit representation of an integer n in radix b as
The above lists all summands of order 6 or lower (i.e. those containing 6 or fewer X 's and Y 's). The X ↔ Y (anti-)/symmetry in alternating orders of the expansion, follows from Z(Y, X) = −Z(−X, −Y). A complete elementary proof of this formula can be found in the article on the derivative of the exponential map.