Paradoxes of set theory
This article contains a discussion of paradoxes of set theory. As with most mathematical paradoxes, they generally reveal surprising and counter-intuitive mathematical results, rather than actual logi...
Nontransitive dice
A set of dice is nontransitive if it contains three dice, A, B, and C, with the property that A rolls higher than B more than half the time, and B rolls higher than C more than half the time, but it i...
Nontransitive dice - Wikipedia
Potato paradox
The Potato Paradox is a mathematical calculation that has a counter-intuitive result. The "paradox" involves dehydrating potatoes by a seemingly minuscule amount, and then calculating a change in mass...
Low birth-weight paradox
The low birth-weight paradox is an apparently paradoxical observation relating to the birth weights and mortality rate of children born to tobacco smoking mothers. Low birth-weight children born to sm...
Kleene-Rosser paradox
In mathematics, the Kleene–Rosser paradox is a paradox that shows that certain systems of formal logic are inconsistent, in particular the version of Curry's combinatory logic introduced in 1930...
Girard's paradox
In the branches of mathematical logic known as proof theory and type theory, a pure type system (PTS), previously known as a generalized type system (GTS), is a form of typed lambda calculus that allo...
Stein's example
Stein's example (or phenomenon or paradox), in decision theory and estimation theory, is the phenomenon that when three or more parameters are estimated simultaneously, there exist combined estimators...
Stein's example - Wikipedia
Exchange paradox
The two envelopes problem, also known as the exchange paradox, is a brain teaser, puzzle, or paradox in logic, probability, and recreational mathematics. It is of special interest in decision theory,...
Exchange paradox - Wikipedia
Friendship paradox
The friendship paradox is the phenomenon first observed by the sociologist Scott L. Feld in 1991 that most people have fewer friends than their friends have, on average. It can be explained as a form ...
Occurrences of Grandi's series

Guido Grandi illustrated the series with a parable involving two brothers who share a gem.Thomson's lamp is a supertask in which a hypothetical lamp is turned on and off infinitely many times in ...
Occurrences of Grandi's series - Wikipedia
Accuracy paradox
The accuracy paradox for predictive analytics states that predictive models with a given level of accuracy may have greater predictive power than models with higher accuracy. It may be better to avoid...
Necktie paradox
The necktie paradox is a puzzle or paradox within the subjectivistic interpretation of probability theory. It is a variation (and historically, the origin) of the two-envelope paradox.
Two men ar...
Ellsberg paradox
The Ellsberg paradox is a paradox in decision theory in which people's choices violate the postulates of subjective expected utility. It is generally taken to be evidence for ambiguity aversion. The p...
Abelson's paradox
Abelson's paradox is an applied statistics paradox identified by Robert P. Abelson. The paradox pertains to a possible paradoxical relationship between the magnitude of the r (i.e., coefficient of det...
Sleeping Beauty problem
The Sleeping Beauty problem is a puzzle in probability theory and formal epistemology in which an ideally rational epistemic agent is to be woken once or twice according to the toss of a coin, and ask...
1 − 2 + 3 − 4 + · · ·
In mathematics, 1 − 2 + 3 − 4 + ··· is the infinite series whose terms are the successive positive integers, given alternating signs. Using sigma summation notation the sum of the first m terms of the...
1 − 2 + 3 − 4 + · · · - Wikipedia
Parrondo's paradox
Parrondo's paradox, a paradox in game theory, has been described as: A combination of losing strategies becomes a winning strategy. It is named after its creator, Juan Parrondo, who discovered the par...
Parrondo's paradox - Wikipedia
Cauchy sequence
In mathematics, a Cauchy sequence ([koʃi]; /ˈkoʊʃiː/ KOH-shee), named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses. More...
Cauchy sequence - Wikipedia
Supertask
In philosophy, a supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time. Supertasks are called "hypertasks" when the number of operations bec...
Freedman's paradox
In statistical analysis, Freedman's paradox, named after David Freedman, describes a problem in model selection whereby predictor variables with no explanatory power can appear artificially important....
Birthday attack
A birthday attack is a type of cryptographic attack that exploits the mathematics behind the birthday problem in probability theory. This attack can be used to abuse communication between two or more ...
Cantor's paradox
In set theory, Cantor's paradox is derivable from the theorem that there is no greatest cardinal number, so that the collection of "infinite sizes" is itself infinite. The difficulty is handled in ax...
Grandi's series
In mathematics, the infinite series 1 − 1 + 1 − 1 + …, also writtenis sometimes called Grandi's series, after Italian mathematician, philosopher, and priest Guido Grandi, who gave a memorable tr...
Grandi's series - Wikipedia
Summation of Grandi's series

The formal manipulations that lead to 1 − 1 + 1 − 1 + · · · being assigned a value of ⁄2 include:These are all legal manipulations for sums of convergent series, but 1 − 1 + 1 − 1 + · · · is not ...
Universal set
In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, the conception of a universal set leads to a paradox (Russell's paradox) and ...
Gabriel's Horn
Gabriel's Horn (also called Torricelli's trumpet) is a geometric figure, which has infinite surface area but finite volume. The name refers to the tradition identifying the Archangel Gabriel as the an...
Gabriel's Horn - Wikipedia