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  2. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    Graphs of y = b x for various bases b: base 10, base e, base 2, base ⁠ 1 / 2 ⁠. Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.

  3. Power of two - Wikipedia

    en.wikipedia.org/wiki/Power_of_two

    The only known powers of 2 with all digits even are 2 1 = 2, 2 2 = 4, 2 3 = 8, 2 6 = 64 and 2 11 = 2048. [12] The first 3 powers of 2 with all but last digit odd is 2 4 = 16, 2 5 = 32 and 2 9 = 512. The next such power of 2 of form 2 n should have n of at least 6 digits.

  4. Exponential function - Wikipedia

    en.wikipedia.org/wiki/Exponential_function

    Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable ⁠ ⁠ is denoted ⁠ ⁡ ⁠ or ⁠ ⁠, with the two notations used interchangeab

  5. Division by zero - Wikipedia

    en.wikipedia.org/wiki/Division_by_zero

    For example, using single-precision IEEE arithmetic, if x = −2 −149, then x/2 underflows to −0, and dividing 1 by this result produces 1/(x/2) = −∞. The exact result −2 150 is too large to represent as a single-precision number, so an infinity of the same sign is used instead to indicate overflow.

  6. Characterizations of the exponential function - Wikipedia

    en.wikipedia.org/wiki/Characterizations_of_the...

    Walter Rudin called it "the most important function in mathematics". [1] It is therefore useful to have multiple ways to define (or characterize) it. Each of the characterizations below may be more or less useful depending on context. The "product limit" characterization of the exponential function was discovered by Leonhard Euler. [2]

  7. Integer overflow - Wikipedia

    en.wikipedia.org/wiki/Integer_overflow

    In particular, multiplying or adding two integers may result in a value that is unexpectedly small, and subtracting from a small integer may cause a wrap to a large positive value (for example, 8-bit integer addition 255 + 2 results in 1, which is 257 mod 2 8, and similarly subtraction 01 results in 255, a two's complement representation ...

  8. Infinity - Wikipedia

    en.wikipedia.org/wiki/Infinity

    In the 17th century, with the introduction of the infinity symbol [1] and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) [2] regarded as infinitely small quantities, but infinity continued to be associated with endless processes.

  9. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    Negative one: −1 ... Foias constant is the unique real number such that if x 1 = α then the sequence diverges to infinity. ... [0; 1, 10, 1, 8, 1, 88, 4, 1, 1, 7 ...