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In mathematical logic, a sentence (or closed formula) [1] of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition , something that must be true or false.
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 consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example, the sentence "a free module is a module that has a basis" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of basis, module, and free module.
Mathematical logic is the study of formal logic within ... It shows that if a particular sentence is true in every model that satisfies a particular set of axioms ...
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 ...
Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).
Consider the formal sentence . For some natural number , =.. This is a single statement using existential quantification. It is roughly analogous to the informal sentence "Either =, or =, or =, or... and so on," but more precise, because it doesn't need us to infer the meaning of the phrase "and so on."
To attempt to define the term would not be doing mathematics, but rather, one would be engaging in a kind of metamathematics (the metalanguage of mathematics), usually mathematical logic. Within mathematical logic, mathematics is usually described as a kind of formal language, and a well-formed expression can be defined recursively as follows: [40]