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If exponentiation is considered as a multivalued function then the possible values of (−1 ⋅ −1) 1/2 are {1, −1}. The identity holds, but saying {1} = {(−1 ⋅ −1) 1/2 } is incorrect. The identity ( e x ) y = e xy holds for real numbers x and y , but assuming its truth for complex numbers leads to the following paradox , discovered ...
Thus the 're-subtracting' of 1 leaves a mantissa ending in '100000000000000' instead of '010111000110010', representing a value of '1.1111111111117289E-4' rounded by Excel to 15 significant digits: '1.11111111111173E-4'. Of course mathematical 1 + x − 1 = x, 'floating point math' is sometimes a little different, that is not to be blamed on ...
Two to the power of n, written as 2 n, is the number of values in which the bits in a binary word of length n can be set, where each bit is either of two values. A word, interpreted as representing an integer in a range starting at zero, referred to as an "unsigned integer", can represent values from 0 (000...000 2) to 2 n − 1 (111...111 2) inclusively.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
The exponential function is the limit [4] [3 ... Exponential functions with bases 2 and 1/2. The base of an exponential function is the base of the exponentiation ...
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Exponential function: raises a fixed number to a variable power. Hyperbolic functions: formally similar to the trigonometric functions. Inverse hyperbolic functions: inverses of the hyperbolic functions, analogous to the inverse circular functions. Logarithms: the inverses of exponential functions; useful to solve equations involving exponentials.
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