How Input and Output Work

Inputconvert from a textual form to an expression
Processingdo computations on the expression
Outputconvert the resulting expression to textual form

Steps in the operation of Mathematica.

When you type something like what Mathematica at first sees is just the string of characters , , . But with the usual way that Mathematica is set up, it immediately knows to convert this string of characters into the expression Power[x, 2].

Then, after whatever processing is possible has been done, Mathematica takes the expression Power[x, 2] and converts it into some kind of textual representation for output.

Mathematica reads the string of characters , , and converts it to the expression Power[x, 2].
In[1]:=
Click for copyable input
Out[1]=
This shows the expression in Fortran form.
In[2]:=
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Out[2]//FortranForm=
FortranForm is just a "wrapper": the value of Out[2] is still the expression Power[x, 2].
In[3]:=
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Out[3]=

It is important to understand that in a typical Mathematica session In[n] and Out[n] record only the underlying expressions that are processed, not the textual representations that happen to be used for their input or output.

If you explicitly request a particular kind of output, say by using TraditionalForm[expr], then what you get will be labeled with Out[n]//TraditionalForm. This indicates that what you are seeing is expr//TraditionalForm, even though the value of Out[n] itself is just expr.

Mathematica also allows you to specify globally that you want output to be displayed in a particular form. And if you do this, then the form will no longer be indicated explicitly in the label for each line. But it is still the case that In[n] and Out[n] will record only underlying expressions, not the textual representations used for their input and output.

This sets to be an expression with FortranForm explicitly wrapped around it.
In[4]:=
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Out[4]//FortranForm=
The result on the previous line is just the expression.
In[5]:=
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Out[5]=
But contains the FortranForm wrapper, and so is displayed in FortranForm.
In[6]:=
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Out[6]//FortranForm=
Wherever appears, it is formatted in FortranForm.
In[7]:=
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Out[7]=
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