In mathematics, an existence theorem is a theorem with a statement beginning 'there exist(s) ..', or more generally 'for all , , ... there exist(s) ...'. That is, in more formal terms of symbolic logic, it is a theorem with a prenex normal form involving the existential quantifier. Many such theorems will not do so explicitly, as usually stated in standard mathematical language. For example, the statement that the sine function is continuous; or any theorem written in big O notation. The quantification can be found in the definitions of the concepts used.