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Logical reasoning happens by inferring a conclusion from a set of premises. [3] Premises and conclusions are normally seen as propositions. A proposition is a statement that makes a claim about what is the case. In this regard, propositions act as truth-bearers: they are either true or false. [18] [19] [3] For example, the sentence "The water ...
In logic, the logical form of a statement is a precisely-specified semantic version of that statement in a formal system.Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system.
A system which is strong k-mixing for all k = 2,3,4,... is called mixing of all orders. It is unknown whether strong 2-mixing implies strong 3-mixing. It is known that strong m -mixing implies ergodicity .
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Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.
[5] [3] System 2, on the other hand, is of more recent evolutionary origin. It is slow and cognitively demanding, but also more flexible and under deliberate control. [5] [3] The dual-process theory posits that system 1 is the default system guiding most of our everyday reasoning in a pragmatic way. But for particularly difficult problems on ...
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
Remark 3. If μ ( S ) < ∞ {\displaystyle \mu (S)<\infty } , the condition that there is a dominating integrable function g {\displaystyle g} can be relaxed to uniform integrability of the sequence ( f n ), see Vitali convergence theorem .