(set theory) A demonstration of a surprising property of infinite sets. Some positive integers are squares while others are not; therefore, all the numbers, including both squares and non-squares, must be more numerous than just the squares; yet for every square there is exactly one positive number that is its square root, and for every number there is exactly one square; hence, there cannot be more of one than of the other.

The observation that at the species level, the incidence of cancer does not appear to correlate with the number of cells in an organism.

(fluid dynamics) The contradiction that, for incompressible and inviscid potential flow, the drag force is zero on a body moving with constant velocity relative to the fluid.

The linguistic paradox that, if there are unnameable things, their existence cannot be indicated without naming them in some way.

(physics) The black hole information paradox.

Synonym of paradox of thrift

(quantum mechanics) A surprising result of applying the Dirac equation to the problem of electron scattering from a potential barrier. In non-relativistic quantum mechanics, electron tunnelling into a barrier is observed, with exponential damping. However, if the potential is of the order of the electron mass, V∼mc², the barrier is nearly transparent; moreover, as the potential approaches infinity, the reflection diminishes and the electron is always transmitted.

(economics) The apparent paradox that a rent seeker wanting political favours can bribe politicians at a cost much lower than the value of the favour to the rent seeker.

A logical paradox resembling the liar paradox but using, instead of a single sentence, an infinite sequence of statements, each referring to the truth values of the later statements in the sequence, and thus attempting to avoid circularity.

(economics) A paradox of economics, stating that an increase in autonomous saving leads to a decrease in aggregate demand and thus a decrease in gross output which will in turn lower total saving: narrowly speaking, total saving may fall because of individuals' attempts to increase their saving, and, broadly speaking, increase in saving may be harmful to an economy.