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It is inspired by the typographic practice of end marks, an element that marks the end of an article. [1] [2] In Unicode, it is represented as character U+220E ∎ END OF PROOF. Its graphic form varies, as it may be a hollow or filled rectangle or square. In AMS-LaTeX, the symbol is automatically appended at the end of a proof environment ...
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
In the AMS Theorem Environment for LaTeX, the hollow square is the default end-of-proof symbol. Unicode explicitly provides the "end of proof" character, U+220E (∎). Some authors use other Unicode symbols to note the end of a proof, including, (U+25AE, a black vertical rectangle), and ‣ (U+2023, a triangular bullet).
LaTeX (/ ˈ l ɑː t ɛ k / ⓘ LAH-tek or / ˈ l eɪ t ɛ k / LAY-tek, [2] [Note 1] often stylized as L a T e X) is a software system for typesetting documents. [3] LaTeX markup describes the content and layout of the document, as opposed to the formatted text found in WYSIWYG word processors like Google Docs, LibreOffice Writer, and Microsoft Word.
This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures; List of data structures; List of derivatives and integrals in alternative calculi; List of equations; List of fundamental theorems; List of hypotheses; List of inequalities; Lists of ...
In Euclid's Elements the theorem is stated in Book IX, Proposition 20: [9] Prime numbers are more than any assigned multitude of prime numbers. Depending on how we formally write the above statement, the usual proof takes either the form of a proof by contradiction or a refutation by contradiction.
These non-probabilistic existence theorems follow from probabilistic results: (a) a number chosen at random (uniformly on (0,1)) is normal almost surely (which follows easily from the strong law of large numbers); (b) some probabilistic inequalities behind the strong law. The existence of a normal number follows from (a) immediately.
CRT – Chinese remainder theorem. csc – cosecant function. (Also written as cosec.) csch – hyperbolic cosecant function. (Also written as cosech.) ctg – cotangent function. (Also written as cot.) curl – curl of a vector field. (Also written as rot.) cvc – covercosine function. (Also written as covercos.) cvs – coversine function.