BUILT-IN MATHEMATICA SYMBOL

NumericFunction

NumericFunction
is an attribute that can be assigned to a symbol f to indicate that

should be considered a numeric quantity whenever all the

are numeric quantities.

Most standard built-in mathematical functions have the attribute NumericFunction.

If you assign the attribute NumericFunction to a function that does not yield numerical values, then NumericQ will give misleading results.

Exp has the NumericFunction attribute:

When Exp has an argument that is a number, constant, or numeric, the result is numeric:

In most cases when NumericQ[expr] gives True, then N[expr] yields an explicit number:

Exp has the NumericFunction attribute:

Out[1]=

When Exp has an argument that is a number, constant, or numeric, the result is numeric:

Out[2]=

In most cases when NumericQ[expr] gives True, then N[expr] yields an explicit number:

Out[3]=

Define

to be a numeric function:

If you have not assigned

to yield numerical values, then NumericQ gives misleading results:

Assign

to evaluate for arguments that are approximate numbers:

The system symbols that are numeric functions:

Define a function that can represent an exact value:

Assign N

to give the derivative with respect to a of the solution of an ODE at

:

Assign f for approximate numbers:

f[1] does not evaluate but represents a number:

It will work with any precision (within reasonable limits!):

A plot of the function: