The Handy Math Answer Book
or it may be a class of entities (objects, houses, cities, men, animals). The predi- cateis the property or mode of existence th ...
MATHEMATICAL AND FORMAL LOGIC What is mathematical logic? Mathematical logic is not the logic of mathematics, but is really the ...
specific mathematical concepts and provides a means to compose proofs of statements. Symbolic logic draws most notably on set th ...
Biconditional—Biconditional (double implication or bi-implication) is true only if the two statements have the same value, eithe ...
AND q,” represented by the symbols or &. The “or” (also called the disjunction oper- ator) is also a binary operator, as in ...
much farther, but it is weaker than certain branches of mathematics, such as arith- metic and set theory. What is a quantifierin ...
matter what variable you chose because it will always be true. Thus, from propositional calculus the sentence, “All humans are m ...
lowed correctly, will lead to a recognizable end result. Simply put, a recipe is an exam- ple of an algorithm. For example, if t ...
Formalismis the idea that mathe- matics is truly formal; therefore, it is only concerned with the algorithmic manipu- lation of ...
rently no single philosophy that truly defines our mathematical and logic foundations, especially when it comes to combining bot ...
sary to an axiomatic system, but consistency is definitely necessary. The opposite of consistency in an axiomatic system is inco ...
What are theorems, corollaries,and lemmas? In mathematics and logic a theoremis a statement demonstrated to be true by accept- e ...
Are there differenttypes of proofs? There are several different types of proofs in mathematical logic. Direct proofsare based on ...
Inductionis a term usually used in cases concerning probability, in which the conclusion can be false even when the premises are ...
What is a fallacy? A fallacy is an incorrect result—in this case, one arrived at through misleading reason- ing when examining a ...
Before an object can travel a distance d,it must keep traveling “in halves”: In terms of the racetrack, in order to reach the en ...
SET THEORY What is set theory? Set theory is the mathematical theory of sets and is associated with logic; it is also considered ...
What is a set? Simply put, a set is a collection of objects or entities; these are called the elementsof the set. The number of ...
What are openand closed sets? Formally, an open setis one in which every element in the set has a neighborin the set or does not ...
Symbol Meaning | such that, as in {x | x is a rational number}, is a set “x, such that x is a rational number” : also used as “s ...
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