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  2. 1, 2, 3, 4 (Plain White T's song) - Wikipedia

    en.wikipedia.org/wiki/1,_2,_3,_4_(Plain_White_T's...

    The music video for the song premiered on the MySpace main page January 16, 2009 [3] and was subsequently released on MTV, MTVU, VH1, Fuse, Music Choice and YouTube. [4] [5] [6] It found success on the weekly VH1 Top 20 Video Countdown, charting over five months straight between January and May, peaking at #5. It was listed on the VH1 Top 40 ...

  3. De Morgan's laws - Wikipedia

    en.wikipedia.org/wiki/De_Morgan's_laws

    Existential generalization / instantiation. In propositional logic and Boolean algebra, De Morgan's laws, [ 1][ 2][ 3] also known as De Morgan's theorem, [ 4] are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician.

  4. Grandi's series - Wikipedia

    en.wikipedia.org/wiki/Grandi's_series

    (4) the result is ⁠ 1 / 2 ⁠ (3) the result is 1 (2) the result is infinite (30) no answer. The researcher, Giorgio Bagni, interviewed several of the students to determine their reasoning. Some 16 of them justified an answer of 0 using logic similar to that of Grandi and Riccati. Others justified ⁠ 1 / 2 ⁠ as being the average of 0 and 1 ...

  5. ILR scale - Wikipedia

    en.wikipedia.org/wiki/ILR_scale

    ILR scale. The Interagency Language Roundtable scale is a set of descriptions of abilities to communicate in a language. It is the standard grading scale for language proficiency in the United States 's Federal-level service. It was originally developed by the Interagency Language Roundtable (ILR), which included representation by United States ...

  6. Cardinal direction - Wikipedia

    en.wikipedia.org/wiki/Cardinal_direction

    The four cardinal directions, or cardinal points, are the four main compass directions: north, south, east, and west, commonly denoted by their initials N, S, E, and W respectively. Relative to north, the directions east, south, and west are at 90 degree intervals in the clockwise direction. The ordinal directions (also called the intercardinal ...

  7. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    For any integer n, n ≡ 1 (mod 2) if and only if 3n + 14 (mod 6). Equivalently, ⁠ n − 1 / 3 ⁠ ≡ 1 (mod 2) if and only if n ≡ 4 (mod 6). Conjecturally, this inverse relation forms a tree except for the 124 loop (the inverse of the 421 loop of the unaltered function f defined in the Statement of the problem section of ...

  8. English grammar - Wikipedia

    en.wikipedia.org/wiki/English_grammar

    English grammar is the set of structural rules of the English language.This includes the structure of words, phrases, clauses, sentences, and whole texts.. This article describes a generalized, present-day Standard English – a form of speech and writing used in public discourse, including broadcasting, education, entertainment, government, and news, over a range of registers, from formal to ...

  9. 1/2 + 1/4 + 1/8 + 1/16 + ⋯ - Wikipedia

    en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/...

    1/2 + 1/4 + 1/8 + 1/16 + ⋯. First six summands drawn as portions of a square. The geometric series on the real line. In mathematics, the infinite series ⁠ 1 2 ⁠ + ⁠ 1 4 ⁠ + ⁠ 1 8 ⁠ + ⁠ 1 16 ⁠ + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation ...

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