# NumericalOrder

NumericalOrder[e1,e2]

gives 1 if e1<e2, -1 if e1>e2, 0 if e1 and e2 are identical or numerically the same and Order[e1,e2] if e1 and e2 are not numerically comparable.

# Details

• NumericalOrder provides a general alternative to canonical order in which numeric expressions, dates and Quantity objects are treated by value, but it is otherwise equivalent to canonical order.
• Quantity expressions with compatible units are compared to each other by magnitude after converting them to a common unit.
• DateObject expressions are compared to each other by AbsoluteTime.
• TimeObject expressions are compared by AbsoluteTime.
• NumericalOrder compares inexact numbers using all available significant digits. Unlike Equal, it does not allow any extra tolerance.
• NumericalOrder can be used as an ordering function in functions like Sort, OrderedQ or Ordering.

# Examples

open allclose all

## Basic Examples(4)

These two numbers are not ordered:

 In[1]:=
 Out[1]=

These two are numerically the same:

 In[2]:=
 Out[2]=

Compare numeric expressions:

 In[1]:=
 Out[1]=

This is not always the same as the canonical order of expressions:

 In[2]:=
 Out[2]=

Compare quantities:

 In[1]:=
 Out[1]=

Compare dates:

 In[1]:=
 Out[1]=