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Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets [4] (finite sets or sets with the same cardinality as the natural numbers). However, there is no exact definition of the term "discrete mathematics". [5]
A mathematical object is an abstract concept arising in mathematics. [1] Typically, a mathematical object can be a value that can be assigned to a symbol, and therefore can be involved in formulas.
The figure shows that 8 can be decomposed into 5 (the number of ways to climb 4 steps, followed by a single-step) plus 3 (the number of ways to climb 3 steps, followed by a double-step). The same reasoning is applied recursively until a single step, of which there is only one way to climb.
The first four partial sums of the series 1 + 2 + 3 + 4 + ⋯.The parabola is their smoothed asymptote; its y-intercept is −1/12. [1]The infinite series whose terms ...
1, 2, 3, 5, 7, 11, 15, 22, ..., omitting the initial value p ( 0 ) = 1 {\displaystyle p(0)=1} of the partition numbers. Each diagonal from upper left to lower right is eventually constant, with the constant parts of these diagonals extending approximately from halfway across each row to its end.
For example: 3 6; 3 6; 3 4.6, tells us there are 3 vertices with 2 different vertex types, so this tiling would be classed as a ‘3-uniform (2-vertex types)’ tiling. Broken down, 3 6 ; 3 6 (both of different transitivity class), or (3 6 ) 2 , tells us that there are 2 vertices (denoted by the superscript 2), each with 6 equilateral 3-sided ...
This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85 5 is only slightly bigger than 2 32. Such method is 6.7% more efficient than MIME-64 which encodes a 24 bit number into 4 printable characters.
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