In Linguistic and Philosophy, a assertion represents a stated regarded or presented as true.

In Logical and Mathematical, an assertion is a mathematical proposal to which it is possible, within the framework of a Théorie, to allot a value of true truth or distorts, but not both (Principe of the third excluded). In other words, we must be able to say without any ambiguity if this formulation is true or false compared to a Système of axioms given and in agreement with a mathematical Logique.

Examples

• 2 + 2 = 4 is a true assertion in the theory of the natural entireties.
• E = 2,71 (where E indicates the base of the Napierian logarithm) is a false assertion in the theory of the real numbers.
• “it will rain tomorrow” is not a mathematical assertion.
• the assertion 1 + 1 = 0 is false in the theory of the entireties but is true in the theory of the numbers modulos 2.

We often intend to say that 2 + 2 = 5 is a false assertion; in fact that implies that 2 and 5 are natural entireties and by using the axioms of the definition of the natural entireties, we lead to an obvious contradiction 1 = 0, for example. But we can make become true this equality by regarding 2 and 5 as equal to 0 and by defining the addition by 0 + 0 = 0. We build in this case another theory; all the problem is to know so then this theory will be of any utility. And will one be able to find much followers of this theory? After all the Italian scientists of the 16th century as Cardan was enhardissaient to work with square roots of negative numbers and noted a certain imaginary complex number wrongly $\backslash \; sqrt\; \{-\; 1\}$; that gave rise to later the theory of the complex numbers.

See too

• Negation (linguistic)