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Two losing gambling games can be set up so that when they are played one after the other, they become winning. There are many ways to construct such scenarios, the simplest ...

In the theory of transfinite ordinal numbers, 1. Every well ordered set has a unique ordinal number, 2. Every segment of ordinals (i.e., any set of ordinals arranged in ...

Consider a game, first proposed by Nicolaus Bernoulli, in which a player bets on how many tosses of a coin will be needed before it first turns up heads. The player pays a ...

An improper use of the symbol sqrt(-1) for the imaginary unit leads to the apparent proof of a false statement. sqrt(-1) = sqrt(-1) (1) sqrt((-1)/1) = sqrt(1/(-1)) (2) ...

Three guests decide to stay the night at a lodge whose rate they are initially told is $30 per night. However, after the guests have each paid $10 and gone to their room, the ...

Curry (1977, p. 5) uses the term pseudoparadox to describe an apparent paradox, such as the catalogue paradox, for which there is no underlying actual contradiction.

Zeno's paradoxes are a set of four paradoxes dealing with counterintuitive aspects of continuous space and time. 1. Dichotomy paradox: Before an object can travel a given ...

A strange loop is a phenomenon in which, whenever movement is made upwards or downwards through the levels of some hierarchical system, the system unexpectedly arrives back ...

Let R be the set of all sets which are not members of themselves. Then R is neither a member of itself nor not a member of itself. Symbolically, let R={x:x not in x}. Then R ...

There are two similar but distinct concepts related to equidecomposability: "equidecomposable" and "equidecomposable by dissection." The difference is in that the pieces ...