information:extraction
Infinite domain of discourse

Consider the following statement (using dot notation for multiplication):

This has the appearance of an infinite conjunction of propositions. From the point of view of formal languages, this is immediately a problem, since syntax rules are expected to generate finite words.

The example above is fortunate in that there is a procedure to generate all the conjuncts. However, if an assertion were to be made about every irrational number, there would be no way to enumerate all the conjuncts, since irrationals cannot be enumerated. A succinct, equivalent formulation which avoids these problems uses universal quantification:

A similar analysis applies to the disjunction,

which can be rephrased using existential quantification: