We have seen how to add a function and a scalar and how to build a function of two variables from two functions of one variable. Let's now focus on the general mechanism that makes this possible. The general mechanism consists of two steps: reshaping and extending.
First, the function 
is reshaped to the function 
, which takes two arguments. One of these arguments is a dummy argument, which we take to be zero, as a convention:
Mathematically, the domain of the definition of 
is now 
Then the function 
is reshaped in a way similar to:
Now both 
and 
take two arguments, although one of them is always zero. We proceed to the next step, extending. It is the same step that converted a constant into a constant function.
The function 
is extended to:
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The function 
is extended to:
Now the function of two variables, 
, which was sloppily defined by 
, may be defined without reference to its arguments:
For...
