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For example, using single-precision IEEE arithmetic, if x = −2 −149, then x/2 underflows to −0, and dividing 1 by this result produces 1/(x/2) = −∞. The exact result −2 150 is too large to represent as a single-precision number, so an infinity of the same sign is used instead to indicate overflow.
For x > 1 let π 0 (x) = π(x) − 1 / 2 when x is a prime number, and π 0 (x) = π(x) otherwise. Bernhard Riemann, in his work On the Number of Primes Less Than a Given Magnitude, proved that π 0 (x) is equal to [9] Riemann's explicit formula using the first 200 non-trivial zeros of the zeta function
With the exceptions of 1, 8 and 144 (F 1 = F 2, F 6 and F 12) every Fibonacci number has a prime factor that is not a factor of any smaller Fibonacci number (Carmichael's theorem). [57] As a result, 8 and 144 ( F 6 and F 12 ) are the only Fibonacci numbers that are the product of other Fibonacci numbers.
The SI unit of kinematic viscosity is square meter per second (m 2 /s), whereas the CGS unit for kinematic viscosity is the stokes (St, or cm 2 ·s −1 = 0.0001 m 2 ·s −1), named after Sir George Gabriel Stokes. [29] In U.S. usage, stoke is sometimes used as the singular form.
However, when (n + 1)p is an integer and p is neither 0 nor 1, then the distribution has two modes: (n + 1)p and (n + 1)p − 1. When p is equal to 0 or 1, the mode will be 0 and n correspondingly. These cases can be summarized as follows:
1998 – Deep Space 1 is launched to explore the asteroid belt and test new spacecraft technologies. 2003 – Concorde makes its last commercial flight. 2004 – Arsenal Football Club loses to Manchester United, ending a row of unbeaten matches at 49 matches, which is the record in the Premier League.
Beginning on 20 November 1923, 1,000,000,000,000ℳ (10 12 ℳ, 1 trillion marks) were exchanged for 1 Rentenmark, so that RM 4.2 was worth 1 US dollar, exactly the same rate the mark had in 1914. [57] First phase: Start and end date: January 1920 – January 1920; Peak month and rate of inflation: January 1920, 56.9%; Second phase:
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8 Week 9 Week 10 Week 11 Week 12 Week 13 Week 14 Week 15 Day 1 Day 2 Day 5 Day 8 Day 12 Day 15 Day 19 Day 22 Day 26 Day 29 Day 31 Day 36 Day 40 Day 43 Day 45 Nominees for Captaincy: No Captain: All housemates Not eligible: Deepak Jacquline Pavithra Sathya Soundariya Vishal Not eligible ...
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