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overlapping antonyms, a pair of comparatives in which one, but not the other, implies the positive: An example is "better" and "worse". The sentence "x is better than y" does not imply that x is good, but "x is worse than y" implies that x is bad. Other examples are "faster" and "slower" ("fast" is implied but not "slow") and "dirtier" and ...
The same term can also be used more informally to refer to something "standard" or "classic". For example, one might say that Euclid's proof is the "canonical proof" of the infinitude of primes. There are two canonical proofs that are always used to show non-mathematicians what a mathematical proof is like:
See § Brackets for examples of use. Most symbols have two printed versions. They can be displayed as Unicode characters, or in LaTeX format. With the Unicode version, using search engines and copy-pasting are easier. On the other hand, the LaTeX rendering is often much better (more aesthetic), and is generally considered a standard in mathematics.
Shows that a sentence can be paradoxical even if it is not self-referring and does not use demonstratives or indexicals. Yablo's paradox: An ordered infinite sequence of sentences, each of which says that all following sentences are false. While constructed to avoid self-reference, there is no consensus whether it relies on self-reference or not.
Īhām, ambiguity used as a literary device in Middle Eastern poetry-onym, suffix denoting a class of names; Oxymoron, contradiction used as a figure of speech; Semantics; Skunked term, a term that becomes difficult to use because it is evolving from one meaning to another, or is otherwise controversial
Also called infinitesimal calculus A foundation of calculus, first developed in the 17th century, that makes use of infinitesimal numbers. Calculus of moving surfaces an extension of the theory of tensor calculus to include deforming manifolds. Calculus of variations the field dedicated to maximizing or minimizing functionals. It used to be called functional calculus. Catastrophe theory a ...
The traditional notations used in the previous section do not distinguish the original function : from the image-of-sets function : (); likewise they do not distinguish the inverse function (assuming one exists) from the inverse image function (which again relates the powersets). Given the right context, this keeps the notation light and ...
The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings.