Search results
Results From The WOW.Com Content Network
Consider the ring A = R[x,y,z] of polynomials in three variables over the real numbers and its field of fractions M = R(x,y,z). The projective dimension of M as A -module is either 2 or 3, but it is independent of ZFC whether it is equal to 2; it is equal to 2 if and only if CH holds.
In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "the house is white" and "the house is not white" are mutually exclusive.
In logic, two propositions and are mutually exclusive if it is not logically possible for them to be true at the same time; that is, () is a tautology. To say that more than two propositions are mutually exclusive, depending on the context, means either 1. "() () is a tautology" (it is not logically possible for more than one proposition to be true) or 2. "() is a tautology" (it is not ...
In probability theory, the complement of any event A is the event [not A], i.e. the event that A does not occur. [1] The event A and its complement [not A] are mutually exclusive and exhaustive. Generally, there is only one event B such that A and B are both mutually exclusive and exhaustive; that event is the complement of A.
Unlike modus ponens and modus ponendo tollens, with which it should not be confused, disjunctive syllogism is often not made an explicit rule or axiom of logical systems, as the above arguments can be proven with a combination of reductio ad absurdum and disjunction elimination. Other forms of syllogism include: hypothetical syllogism
The formula calculator concept can be applied to all types of calculator, including arithmetic, scientific, statistics, financial and conversion calculators. The calculation can be typed or pasted into an edit box of: A software package that runs on a computer, for example as a dialog box. An on-line formula calculator hosted on a web site.
In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events , hence the name.
A free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol.