In mathematics, the identifiability condition is defined as
which says that if a function evaluates the same then the arguments must be the same. I.e., a function is "identifiable" iff it is one-to-one. The article on injective functions deals with this same topic more abstractly.
Example 1
Let the function be the sine function.
This function does not satisfy the condition when the parameter is allowed to take any real number.
However, if the parameter is restricted to [0,2π) then it satisifies the condition
Example 2
Let the function be y = f(x) = x3.
This function clearly satisfies the condition as it is a one-to-one function.
Example 3
Let the function be the normal distribution with zero mean.
For a fixed random value and nonfixed variance this function satisfies the condition
