text: Both arrows are not well-defined as predicates in logic of existence, which normally uses the semantics of total functions. Term f(x) is a term and it has some value for example , but in the same time  can be a legitimate value of a function.
  Therefore the predicate "defined" doesn't respect equality, therefore it is not well-defined.
  The logic of definiteness has different predicate calculus, for example specialization of a formula with universal quantifier requires the term to be well-defined.
  Moreover, it requires introduction of a quasi-equality notion, which makes necessary the reformulation of the axioms.
  The symbols of infinity
  In analysis, measure theory and other mathematical disciplines, the symbol  is frequently used to denote an infinite pseudo-number, along with its negative, . The symbol has no well-defined meaning by itself, but an expression like  is shorthand for a divergent sequence, which at some point is eventually larger than any given real number.
  Performing standard arithmetic operations with the symbols  is undefined. Some extensions, though, define the following conventions of addition and multiplication:
  for all .
  for all .
  for all .
  No sensible extension of addition and multiplication with  exists in the following cases:
  (although in measure theory, this is often defined as )
  For more detail, see extended real number line.