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ISBN 0-691-11485-4. Guilin Liu, Lisheng Feng, Airong Jiang, and Xiaohui Zheng. (2003). The Development of E-mathematics Resources at Tsinghua University Library (THUL)," in Electronic Information and Communication in Mathematics, 1–13. Edited by Fengshen Bai and Bernd Wegner. Berlin: Springer. ISBN 3-540-40689-1.
MS. Kennicott 3, created in 1299. Shows the beginning of Numbers with its first word illustrated with calligraphy: וידבר Way-ḏabbêr, "And He spoke…" Most commentators divide Numbers into three sections based on locale (Mount Sinai, Kadesh-Barnea and the plains of Moab), linked by two travel sections; [7] an alternative is to see it as structured around the two generations of ...
The New King James Version (NKJV) is a translation of the Bible in contemporary English. Published by Thomas Nelson, the complete NKJV was released in 1982.With regard to its textual basis, the NKJV relies on a modern critical edition (the Biblia Hebraica Stuttgartensia) for the Old Testament, [1] while opting to use the Textus Receptus for the New Testament.
Giuseppe Peano First recorded usage of the symbol ϵ for set membership.. The 1889 treatise Arithmetices principia, nova methodo exposita (The principles of arithmetic, presented by a new method) by Giuseppe Peano is widely considered to be a seminal document in mathematical logic and set theory, [1] [2] introducing what is now the standard axiomatization of the natural numbers, and known as ...
The final digit of a triangular number is 0, 1, 3, 5, 6, or 8, and thus such numbers never end in 2, 4, 7, or 9. A final 3 must be preceded by a 0 or 5; a final 8 must be preceded by a 2 or 7. In base 10, the digital root of a nonzero triangular number is always 1, 3, 6, or 9. Hence, every triangular number is either divisible by three or has a ...
The only odd practical number is 1, because if is an odd number greater than 2, then 2 cannot be expressed as the sum of distinct divisors of . More strongly, Srinivasan (1948) observes that other than 1 and 2, every practical number is divisible by 4 or 6 (or both).
There usually are fewer 2-digit Friedman numbers than 3-digit and more in any given base, but the 2-digit ones are easier to find. If we represent a 2-digit number as mb + n, where b is the base and m, n are integers from 0 to b−1, we need only check each possible combination of m and n against the equalities mb + n = m n, and mb + n = n m to see which ones are true.
When speaking the numbers in fractions, the spatial/chronological numbering system is used for denominators larger than 2 (2 as the denominator of a fraction is "half" rather than "second"), with a denominator of 4 sometimes spoken as "quarter" rather than "fourth".