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Arnauld's paradox states that if negative numbers exist, then (-1)/1 must equal 1/(-1), which asserts that the ratio of a smaller to a larger quantity equals the ratio of the ...

It is possible to describe a set of positive integers that cannot be listed in a book containing a set of counting numbers on each consecutively numbered page. Another form ...

A paradox in decision theory. Given two boxes, B1 which contains $1000 and B2 which contains either nothing or a million dollars, you may pick either B2 or both. However, at ...

A lamp is turned on for 1/2 minute, off for 1/4 minute, on for 1/8 minute, etc. At the end of one minute, the lamp switch will have been moved aleph_0 times, where aleph_0 is ...

Consider the probability Q_1(n,d) that no two people out of a group of n will have matching birthdays out of d equally possible birthdays. Start with an arbitrary person's ...

Birthday attacks are a class of brute-force techniques used in an attempt to solve a class of cryptographic hash function problems. These methods take advantage of functions ...

In identical experiments, an Allais paradox occurs when the addition of an independent event influences choice behavior. Consider the choices in the following table (Kahneman ...

In Robert Louis Stevenson's "bottle imp paradox," you are offered the opportunity to buy, for whatever price you wish, a bottle containing a genie who will fulfill your every ...

The above two figures are rearrangements of each other, with the corresponding triangles and polyominoes having the same areas. Nevertheless, the bottom figure has an area ...

First stated in 1924, the Banach-Tarski paradox states that it is possible to decompose a ball into six pieces which can be reassembled by rigid motions to form two balls of ...