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An n-bit LUT can encode any n-input Boolean function by storing the truth table of the function in the LUT. This is an efficient way of encoding Boolean logic functions, and LUTs with 4-6 bits of input are in fact the key component of modern field-programmable gate arrays (FPGAs) which provide reconfigurable hardware logic capabilities.
In some languages, it is possible to create a nested function that accesses a set of parameters from the outer function, that is a closure, and have that function be the outer function's return value. Thus it is possible to return a function that is set to fulfill a certain task with little or no further parameters given to it, which can ...
In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition. [1] This sort of quantification is known as uniqueness quantification or unique existential quantification, and is often denoted with the symbols "∃!"
This particular example is true, because 5 is a natural number, and when we substitute 5 for n, we produce the true statement =. It does not matter that " n × n = 25 {\displaystyle n\times n=25} " is true only for that single natural number, 5; the existence of a single solution is enough to prove this existential quantification to be true.
In section 6.2 of the old IEEE 754-2008 standard, there are two anomalous functions (the maxNum and minNum functions, which return the maximum and the minimum, respectively, of two operands that are expected to be numbers) that favor numbers — if just one of the operands is a NaN then the value of the other operand is returned.
The relation (f m) n (x) = (f n) m (x) = f mn (x) also holds, analogous to the property of exponentiation that (a m) n = (a n) m = a mn. The sequence of functions f n is called a Picard sequence, [8] [9] named after Charles Émile Picard. For a given x in X, the sequence of values f n (x) is called the orbit of x.
Again we expect that there will be not just one but many primes between n 2 and (n + 1) 2, but in this case the PNT does not help: the number of primes up to x 2 is asymptotic to x 2 /log(x 2) while the number of primes up to (x + 1) 2 is asymptotic to (x + 1) 2 /log((x + 1) 2), which is asymptotic to the estimate on primes up to x 2.
In mathematics, the limit of a sequence of sets,, … (subsets of a common set ) is a set whose elements are determined by the sequence in either of two equivalent ways: (1) by upper and lower bounds on the sequence that converge monotonically to the same set (analogous to convergence of real-valued sequences) and (2) by convergence of a sequence of indicator functions which are themselves ...