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Hasse diagram of the natural numbers, partially ordered by "x≤y if x divides y".The numbers 4 and 6 are incomparable, since neither divides the other. In mathematics, two elements x and y of a set P are said to be comparable with respect to a binary relation ≤ if at least one of x ≤ y or y ≤ x is true.
To prove that this condition is sufficient to guarantee existence of a compatible second-order tensor field, we start with the assumption that a field exists such that =. We will integrate this field to find the vector field v {\displaystyle \mathbf {v} } along a line between points A {\displaystyle A} and B {\displaystyle B} (see Figure 2), i.e.,
An example is Enrico Fermi's estimate of the strength of the atomic bomb that detonated at the Trinity test, based on the distance traveled by pieces of paper he dropped from his hand during the blast. Fermi's estimate of 10 kilotons of TNT was well within an order of magnitude of the now-accepted value of 21 kilotons. [1] [2] [3]
For a given congruence ~ on A, the set A / ~ of equivalence classes can be given the structure of an algebra in a natural fashion, the quotient algebra. The function that maps every element of A to its equivalence class is a homomorphism, and the kernel of this homomorphism is ~. The lattice Con(A) of all congruence relations on an algebra A is ...
The smallest friendly number is 6, forming for example, the friendly pair 6 and 28 with abundancy σ(6) / 6 = (1+2+3+6) / 6 = 2, the same as σ(28) / 28 = (1+2+4+7+14+28) / 28 = 2. The shared value 2 is an integer in this case but not in many other cases. Numbers with abundancy 2 are also known as perfect numbers. There are several unsolved ...
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.