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For various reasons, individuals are known to attribute significance to dates and numbers. One notable example is the significance given to "the eleventh hour of the eleventh day of the eleventh month," which corresponds to 11:00 a.m. (Paris time) on 11 November 1918.
The 144,000 (Rev. 7:4; 14:1, 3) are the multiples of 12 x 12 x 10 x 10 x 10, a symbolic number that signifies the total number (tens) of the people of God (twelves). The 12,000 stadia (12 x 10 x 10 x 10) of the walls of the New Jerusalem in Rev. 21:16 represent an immense city that can house the total number (tens) of God's people (twelves).
For any integer n, n ≡ 1 (mod 2) if and only if 3n + 1 ≡ 4 (mod 6). Equivalently, n − 1 / 3 ≡ 1 (mod 2) if and only if n ≡ 4 (mod 6). Conjecturally, this inverse relation forms a tree except for the 1–2–4 loop (the inverse of the 4–2–1 loop of the unaltered function f defined in the Statement of the problem section of ...
where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = 1 / 6 , B 4 = − + 1 / 30 , and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]
The idea becomes clearer by considering the general series 1 − 2x + 3x 2 − 4x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.
[2] [3] Most ambigrams are visual palindromes that rely on some kind of symmetry, and they can often be interpreted as visual puns. [4] The term was coined by Douglas Hofstadter in 1983–1984. [2] [5] Most often, ambigrams appear as visually symmetrical words. When flipped, they remain unchanged, or they mutate to reveal another meaning.
The first: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 (sequence A005408 in the OEIS). All integers are either even or odd. All integers are either even or odd. A square has even multiplicity for all prime factors (it is of the form a 2 for some a ).
6 1 2 1 1 −1 4 5 9. and would be written in modern notation as 6 1 / 4 , 1 1 / 5 , and 2 − 1 / 9 (i.e., 1 8 / 9 ). The horizontal fraction bar is first attested in the work of Al-Hassār (fl. 1200), [35] a Muslim mathematician from Fez, Morocco, who specialized in Islamic inheritance jurisprudence.