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In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. For the categorical proposition All S are P, the converse is All P are S. Either way, the truth of the converse is generally independent from that of ...
The converse is "If a polygon has four sides, then it is a quadrilateral. " Again, in this case, unlike the last example, the converse of the statement is true. The negation is " There is at least one quadrilateral that does not have four sides.
The converse relation does satisfy the (weaker) axioms of a semigroup with involution: () = and () =. [12] Since one may generally consider relations between different sets (which form a category rather than a monoid, namely the category of relations Rel ), in this context the converse relation conforms to the axioms of a dagger category (aka ...
The above concept of relation [a] has been generalized to admit relations between members of two different sets (heterogeneous relation, like "lies on" between the set of all points and that of all lines in geometry), relations between three or more sets (finitary relation, like "person x lives in town y at time z "), and relations between ...
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
Conversely, analytic geometry is the association of points on lines (especially axis lines) to real numbers such that geometric displacements are proportional to differences between corresponding numbers. The informal descriptions above of the real numbers are not sufficient for ensuring the correctness of proofs of theorems involving real numbers.