The language used to formulate a mathematical theory is called the object language to contrast it from the metalanguage used for the discourse.
The most widely used object language is the first-order logic. The
metalanguage could be English or other natural languages plus
mathematical symbols such as .
In induction proofs, one might encounter “the first symbol in the formula is ;” we know that the first symbol is indeed and not because is a symbol in our metalanguage. Similarly, “the third symbol is ” and not because is a symbol in our metalanguage.
and are members of the metalanguage, not of object language.
Parallel with the notion of metalanguage is metatheorem. “ if ” is a metatheorem.
- 1 Schechter, E., Handbook of Analysis and Its Foundations, 1st ed., Academic Press, 1997.
|Date of creation||2013-03-22 18:06:05|
|Last modified on||2013-03-22 18:06:05|
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