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  2. Word equation - Wikipedia

    en.wikipedia.org/wiki/Word_equation

    A word equation is a formal equality:= = between a pair of words and , each over an alphabet comprising both constants (c.f. ) and unknowns (c.f. ). [1] An assignment of constant words to the unknowns of is said to solve if it maps both sides of to identical words.

  3. Natural logarithm - Wikipedia

    en.wikipedia.org/wiki/Natural_logarithm

    For example, ln 7.5 is 2.0149..., because e 2.0149... = 7.5. The natural logarithm of e itself, ln e, is 1, because e 1 = e, while the natural logarithm of 1 is 0, since e 0 = 1. The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a [4] (with the area being negative when 0 < a < 1 ...

  4. List of limits - Wikipedia

    en.wikipedia.org/wiki/List_of_limits

    If is expressed in radians: ⁡ = ⁡ ⁡ = ⁡ These limits both follow from the continuity of sin and cos. ⁡ =. [7] [8] Or, in general, ⁡ =, for a not equal to 0. ⁡ = ⁡ =, for b not equal to 0.

  5. Fine and Wilf's theorem - Wikipedia

    en.wikipedia.org/wiki/Fine_and_Wilf's_theorem

    In combinatorics on words, Fine and Wilf's theorem is a fundamental result describing what happens when a long-enough word has two different periods (i.e., distances at which its letters repeat). [ 1 ] [ 2 ] Informally, the conclusion is that such words w {\displaystyle w} have also a third, shorter period.

  6. Continued fraction - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction

    In the first of these equations the ratio tends toward ⁠ A n / B n ⁠ as z tends toward zero. In the second, the ratio tends toward ⁠ A n / B n ⁠ as z tends to infinity. This leads us to our first geometric interpretation. If the continued fraction converges, the successive convergents ⁠ A n / B n ⁠ are eventually arbitrarily close ...

  7. Help:Displaying a formula - Wikipedia

    en.wikipedia.org/wiki/Help:Displaying_a_formula

    If nothing is specified, the equation is rendered in the same display style as "block", but without using a new paragraph. If the equation does appear on a line by itself, it is not automatically indented. The sum = converges to 2. The next line-width is disturbed by large operators. Or: The sum