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Recamán's sequence: 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence. A005132: Look-and ...
Success in middle-school mathematics courses is correlated with having an understanding of numbers by the start of first grade. [42] This traditional sequence assumes that students will pursue STEM programs in college, though, in practice, only a minority are willing and able to take this option. [4] Often a course in Statistics is also offered ...
[10] [11] The scope and sequence of the curriculum was developed by eighteen mathematicians from the U.S. and Europe in 1966 and subsequently refined in experimental course material by mathematical educators with high school level teaching experience. [9]
The sequence of numbers involved is sometimes referred to as the hailstone sequence, hailstone numbers or hailstone numerals (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), [5] or as wondrous numbers. [6] Paul Erdős said about the Collatz conjecture: "Mathematics may not be ready for such ...
In a topos mathematics can be done. In a higher topos not only mathematics can be done but also "n-geometry", which is higher homotopy theory. The topos hypothesis is that the (n+1)-category nCat is a Grothendieck (n+1)-topos. Higher topos theory can also be used in a purely algebro-geometric way to solve various moduli problems in this setting.
In mathematics, more specifically in general topology and related branches, a net or Moore–Smith sequence is a function whose domain is a directed set. The codomain of this function is usually some topological space. Nets directly generalize the concept of a sequence in a metric space.
CTC refers to the outputs and scoring, and is independent of the underlying neural network structure. It was introduced in 2006. [2] The input is a sequence of observations, and the outputs are a sequence of labels, which can include blank outputs. The difficulty of training comes from there being many more observations than there are labels.
A sequence space is any linear subspace of . As a topological space, K N {\displaystyle \mathbb {K} ^{\mathbb {N} }} is naturally endowed with the product topology . Under this topology, K N {\displaystyle \mathbb {K} ^{\mathbb {N} }} is Fréchet , meaning that it is a complete , metrizable , locally convex topological vector space (TVS).