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The notion that you must define something before you can use it is ingrained \
deeply into the brains of most science folk! If you program in C or Fortran \
you will know what problems you can encounter if you use undefined things. \
This creates a culture in which many people start their work with a whole \
bunch of assignments to variables. This is unfortunate for at least two \
reasons:

Leaving things undefined can produce many interesting results. For example, \
using an undefined function, f (say) you can obtain a wealth of interesting \
results, such as:\
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Cell["\<\
These results are, of course, true for an arbitrary repeatedly diferentiable \
function f.

Undefined functions and variables also help you explore the operation of many \
Mathematica operations. For example:\
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Often it is better to work with expressions with undefined variables and \
functions and use /. to replace them with numeric values only when required. \
What is the point of going to the trouble to discover the notation for \
Planck's constant, only to define it away:\
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Cell["\<\
Any output from Mathematica involving this constant will be reduced to a \
meaningless number. Think of the way you would probably perform a hand \
calculation.

This brings me to the second \[Section]Emphasise[\"big problem\"] with an \
over-use of definitions.  Variable definitions have a habit of hanging around \
while you use Mathematica on an unrelated calculation. This can be extremely \
dangerous (the type of danger obviously depends on your area of \
application!). Suppose you have inadvertently set x=10 as part of some \
calculation and you then move on to something else. The chances are high that \
you will use the variable x again, but it will be immediately replaced by its \
'value': 10. \
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