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mynameisfunk
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Can anyone show me a proof of 1/4 being in the cantor set?? My prof said it is, I read it is, i saw no proof though. Not in my text anyway, also couldn't find it on google.
The Cantor set is a mathematical construct created by German mathematician Georg Cantor in the late 19th century. It is a set of points on a line that is constructed by repeatedly removing the middle third of line segments.
The Cantor set is related to 1/4 because after the first iteration of removing the middle third of line segments, 1/4 of the original line remains. This pattern continues with each iteration, resulting in an infinite number of line segments that are 1/4 of the previous iteration.
A number is considered to be in the Cantor set if it can be expressed as a ternary (base 3) decimal with only the digits 0 and 2. This means that the number can be written as a sum of fractions with powers of 3 in the denominator, where each fraction has a coefficient of either 0 or 2.
The Cantor set is considered to be a fractal, because it has a self-similar structure that repeats itself infinitely at smaller and smaller scales. This property is similar to other well-known fractals, such as the Mandelbrot set and the Koch curve.
The Cantor set has various applications in mathematics, physics, and computer science. In mathematics, it is used to study properties of fractals and chaotic systems. In physics, it has been used to model the structure of certain materials and the dynamics of certain physical systems. In computer science, it has been used in data compression algorithms and to generate random numbers.