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The answer is yes, because for every natural number n there is a square number n 2, and likewise the other way around. The answer is no, because the squares are a proper subset of the naturals: every square is a natural number but there are natural numbers, like 2, which are not squares of natural numbers.
In mathematical analysis, the staircase paradox is a pathological example showing that limits of curves do not necessarily preserve their length. [1] It consists of a sequence of "staircase" polygonal chains in a unit square , formed from horizontal and vertical line segments of decreasing length, so that these staircases converge uniformly to ...
Chessboard paradox. The chessboard paradox [1] [2] or paradox of Loyd and Schlömilch [3] is a falsidical paradox based on an optical illusion. A chessboard or a square with a side length of 8 units is cut into four pieces. Those four pieces are used to form a rectangle with side lengths of 13 and 5 units.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Buttered cat paradox: Humorous example of a paradox from contradicting proverbs. Intentionally blank page: Many documents contain pages on which the text "This page intentionally left blank" is printed, thereby making the page not blank. Metabasis paradox: Conflicting definitions of what is the best kind of tragedy in Aristotle's Poetics.
It was suggested to Russell as an alternative form of Russell's paradox, [1] which Russell had devised to show that set theory as it was used by Georg Cantor and Gottlob Frege contained contradictions. However, Russell denied that the Barber's paradox was an instance of his own: That contradiction [Russell's paradox] is extremely interesting.
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Aristotle's wheel paradox is a paradox or problem appearing in the pseudo-Aristotelian Greek work Mechanica. It states as follows: A wheel is depicted in two-dimensional space as two circles . Its larger, outer circle is tangential to a horizontal surface (e.g. a road that it rolls on), while the smaller, inner one has the same center and is ...
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