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===Veridical paradox=== {{See also|Veridicality}} A ''veridical paradox'' produces a result that appears counter to [[intuition]], but is demonstrated to be true nonetheless: * That the Earth is an [[Spherical Earth|approximately spherical object]] that is [[heliocentrism|rotating and in rapid motion around the Sun]], rather than the apparently obvious and common-sensical appearance of the Earth as a stationary [[flat Earth|approximately flat plane]] illuminated by a Sun that [[geocentrism|rises and falls throughout the day]]. * [[Condorcet paradox|Condorcet's paradox]] demonstrates the surprising result that [[majority rule]] can be self-contradictory, i.e. it is possible for a majority of voters to support some outcome other than the one chosen (regardless of the outcome itself). * The [[Monty Hall paradox]] (or equivalently [[three prisoners problem]]) demonstrates that a decision that has an intuitive fifty–fifty chance can instead have a provably different probable outcome. Another veridical paradox with a concise mathematical proof is the [[Birthday problem|birthday paradox]]. * In 20th-century science, [[Hilbert's paradox of the Grand Hotel]] or the [[Ugly duckling theorem]] are famously vivid examples of a theory being taken to a logical but paradoxical end. * The divergence of the [[harmonic series (mathematics)|harmonic series]]:<math>\sum_{n=1}^\infty\frac{1}{n} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \cdots.</math>
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