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In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. [1] Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.
lim sup X n = {0,1} lim inf X n = { } That is, the four elements that do not match the pattern do not affect the lim inf and lim sup because there are only finitely many of them. In fact, these elements could be placed anywhere in the sequence. So long as the tails of the sequence are maintained, the outer and inner limits will be unchanged.
The distribution of X 1 + ⋯ + X n / √ n need not be approximately normal (in fact, it can be uniform). [38] However, the distribution of c 1 X 1 + ⋯ + c n X n is close to (,) (in the total variation distance) for most vectors (c 1, ..., c n) according to the uniform distribution on the sphere c 2 1 + ⋯ + c 2 n = 1.
Lim Hak Tai, SK (simplified Chinese: 林学大; traditional Chinese: 林學大; pinyin: Lín Xué Dà; Pe̍h-ōe-jī: Lîm Ha̍k-tāi; 28 May 1893 – 14 February 1963) was one of Singapore's pioneer artist at the turn of the 20th century, and was the person who inspired the Nanyang School of art form, to reflect the 'Nanyang' (South-east Asia) region, both in painting style and subject matter.