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Excel's storage of numbers in binary format also affects its accuracy. [3] To illustrate, the lower figure tabulates the simple addition 1 + x − 1 for several values of x. All the values of x begin at the 15 th decimal, so Excel must take them into account. Before calculating the sum 1 + x, Excel first approximates x as a binary number
Algebraic number: Any number that is the root of a non-zero polynomial with rational coefficients. Transcendental number: Any real or complex number that is not algebraic. Examples include e and π. Trigonometric number: Any number that is the sine or cosine of a rational multiple of π.
(also written as 0. 9, 0.., or 0.(9)) is a repeating decimal that is an alternate way of writing the number 1. Following the standard rules for representing numbers in decimal notation, its value is the smallest number greater than or equal to every number in the sequence 0.9, 0.99, 0.999, .... It can be proved that this number is 1; that is,
A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758 Extravagant numbers
Thus 123.456 is considered an approximation of any real number greater or equal to 1234555 / 10000 and strictly less than 1234565 / 10000 (rounding to 3 decimals), or of any real number greater or equal to 123456 / 1000 and strictly less than 123457 / 1000 (truncation after the 3. decimal). Digits that suggest a ...
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A perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers; if the sum equals n, then n is a perfect totient number.
Some Greek mathematicians treated the number 1 differently than larger numbers, sometimes even not as a number at all. [c] Euclid, for example, defined a unit first and then a number as a multitude of units, thus by his definition, a unit is not a number and there are no unique numbers (e.g., any two units from indefinitely many units is a 2). [17]