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Pop Quiz: Who said he would rather read the worst book ever written than watch the best movie ever made? Hint: He liked to smoke.
Anyway, these cool links are from the Department of Mindless Entertainment: (1) , (2) , (3) , (4) . Enjoy!
Remember the so-called face on Mars? We now have some : "A perspective view showing the so-called 'Face on Mars' located in the Cydonia region. The image shows a remnant massif thought to have formed via landslides and an early form of debris apron formation. The massif is characterized by a western wall that has moved downslope as a coherent mass. The massif became famous as the 'Face on Mars' in a photo taken on 25 July 1976 by the American Viking 1 Orbiter."
offers true random numbers to anyone on the internet. If you want to know how the numbers are made and what it is that makes them true, read the to randomness and random numbers. All numbers are tested statistically and the results available in . The answers other common questions.
The Cantor set, introduced by German mathematician Georg Cantor, is a construction of a set of points lying on a single line segment, and involving only the real numbers between zero and one.
The Cantor set is created by repeatedly deleting the open middle thirds of a set of line segments. One starts by deleting the open middle third from the interval [0, 1], leaving two line segments: [0, 1/3] U [2/3, 1]. Next, the open middle third of each of these remaining segments is deleted. This process is continued ad infinitum. The Cantor set contains all points in the interval [0, 1] that are not deleted at any step in this infinite process.
It can be shown that there are as many points left behind in this process as there were that were removed, and that therefore, the Cantor set is uncountable. To see this, we show that there is a function f from the Cantor set C to the closed interval [0,1] that is surjective (i.e. f maps from C onto [0,1]) so that the cardinality of C is no less than that of [0,1]. Since C is a subset of [0,1], its cardinality is also no greater, so the two cardinalities must in fact be equal.
