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If only numbers with unique non-zero digits are considered, a three-digit number in base ten can have a digit-sum ranging from 6 = 1+2+3 to 24 = 7+8+9. If these potential digit-sums are used in the formula 2 x digit-sum x 11, the digit-sum of the result will determine whether or not the result is an Osiris number. 1. 2 x 6 x 11 = 132. 2.
Imaginary numbers: Numbers that equal the product of a real number and the imaginary unit , where =. The number 0 is both real and imaginary. The number 0 is both real and imaginary. Complex numbers ( C {\displaystyle \mathbb {C} } ): Includes real numbers, imaginary numbers, and sums and differences of real and imaginary numbers.
6174 is a 7-smooth number, i.e. none of its prime factors are greater than 7. 6174 can be written as the sum of the first three powers of 18: 18 3 + 18 2 + 18 1 = 5832 + 324 + 18 = 6174, and coincidentally, 6 + 1 + 7 + 4 = 18. The sum of squares of the prime factors of 6174 is a square: 2 2 + 3 2 + 3 2 + 7 2 + 7 2 + 7 2 = 4 + 9 + 9 + 49 + 49 ...
The aleph numbers differ from the infinity commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or "increases without bound"), or as an extreme point of the ...
Integer overflow can be demonstrated through an odometer overflowing, a mechanical version of the phenomenon. All digits are set to the maximum 9 and the next increment of the white digit causes a cascade of carry-over additions setting all digits to 0, but there is no higher digit (1,000,000s digit) to change to a 1, so the counter resets to zero.
In a vector space, the additive inverse −v (often called the opposite vector of v) has the same magnitude as v and but the opposite direction. [11] In modular arithmetic, the modular additive inverse of x is the number a such that a + x ≡ 0 (mod n) and always exists. For example, the inverse of 3 modulo 11 is 8, as 3 + 8 ≡ 0 (mod 11). [12]
A number that is non-palindromic in all bases b in the range 2 ≤ b ≤ n − 2 can be called a strictly non-palindromic number. For example, the number 6 is written as "110" in base 2, "20" in base 3, and "12" in base 4, none of which are palindromes. All strictly non-palindromic numbers larger than 6 are prime.
Consider the number 3.1400010000000000000000050000.... 3.14(3 zeros)1(17 zeros)5(95 zeros)9(599 zeros)2(4319 zeros)6... where the digits are zero except in positions n! where the digit equals the nth digit following the decimal point in the decimal expansion of π.