Lecture

Counter-example of basic condition

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Description

This lecture discusses the basic counter-example related to the condition f&C (R) not being sufficient for f to be represented by an entire series, exploring the implications and propositions derived from this scenario.

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Analysis I (part 6) : Study of functions, limited developments

The study of functions is the discussion of some of their properties. To do this, we need certain theorems that allow us, for example, to find the variations of the function under study. We've already seen the theorem of finite increments. In this chapter, we study its generalization. When we study a function, we also want to know how it behaves at infinity. Unfortunately, the limits of some functions can be quite complicated to study, so we introduce the Bernoulli-l'Hospital rule and demonstrate it. This r

Analysis I

This course covers : Part 1: Prelude, basic concepts, real numbers. Part 2: Introduction to complex numbers. Part 3: Real number sequences I and II. Part 4: Limit of a function, continuous functions. Part 5: Continuous functions and derivable functions, the derivative function. Part 6: Studies of functions, limited developments. Part 7: Indefinite and definite integrals, integration (selected chapters).

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Proposition

A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity. Propositions are also often characterized as being the kind of thing that declarative sentences denote. For instance the sentence "The sky is blue" denotes the proposition that the sky is blue. However, crucially, propositions are not themselves linguistic expressions.

Propositional calculus

Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives. Propositions that contain no logical connectives are called atomic propositions.

Propositional formula

In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, or a sentential formula. A propositional formula is constructed from simple propositions, such as "five is greater than three" or propositional variables such as p and q, using connectives or logical operators such as NOT, AND, OR, or IMPLIES; for example: (p AND NOT q) IMPLIES (p OR q).

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In mathematical logic, a propositional variable (also called a sentential variable or sentential letter) is an input variable (that can either be true or false) of a truth function. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher-order logics. Formulas in logic are typically built up recursively from some propositional variables, some number of logical connectives, and some logical quantifiers.

Propositional attitude

A propositional attitude is a mental state held by an agent or organism toward a proposition. In philosophy, propositional attitudes can be considered to be, neurally-realized causally efficacious content-bearing internal states (personal principles/values). Linguistically, propositional attitudes are denoted by a verb (e.g. "believed") governing an embedded "that" clause, for example, 'Sally believed that she had won'. Propositional attitudes are often assumed to be the fundamental units of thought and their contents, being propositions, are true or false from the perspective of the person.

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