Search results
Results from the WOW.Com Content Network
In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. [1] [2] It is denoted by π(x) (unrelated to the number π). A symmetric variant seen sometimes is π 0 (x), which is equal to π(x) − 1 ⁄ 2 if x is exactly a prime number, and equal to π(x) otherwise.
To be precise, what is sought are often not necessarily actual values, but, more in general, expressions. A solution of the inequation is an assignment of expressions to the unknowns that satisfies the inequation(s); in other words, expressions such that, when they are substituted for the unknowns, make the inequations true propositions.
The phenomenon that π 4,3 (x) is ahead most of the time is called Chebyshev's bias. The prime number race generalizes to other moduli and is the subject of much research; Pál Turán asked whether it is always the case that π c,a (x) and π c,b (x) change places when a and b are coprime to c. [34] Granville and Martin give a thorough ...
The same is true for not less than, . The notation a ≠ b means that a is not equal to b; this inequation sometimes is considered a form of strict inequality. [4] It does not say that one is greater than the other; it does not even require a and b to be member of an ordered set.
Similarly, with 3*x++, where though the post-fix ++ is designed to act AFTER the entire expression is evaluated, the precedence table makes it clear that ONLY x gets incremented (and NOT 3*x). In fact, the expression (tmp=x++, 3*tmp) is evaluated with tmp being a temporary value. It is functionally equivalent to something like (tmp=3*x, ++x, tmp).
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]
For p an odd prime, count all digits greater than (p + 1) / 2; also count digits equal to (p + 1) / 2 unless final; and count digits equal to (p − 1) / 2 if not final and the next digit is counted. [2] The only known odd Catalan numbers that do not have last digit 5 are C 0 = 1, C 1 = 1, C 7 = 429, C 31, C 127 and C 255.
See also: the {{}} template. The #if function selects one of two alternatives based on the truth value of a test string. {{#if: test string | value if true | value if false}} As explained above, a string is considered true if it contains at least one non-whitespace character.