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an unassuming equation, with a simple graph.
The graph and equation are a pair: the graph contains the
points for which the equation is satisfied.
Early in school, as our teachers instill into us the logics
of mathematics and geometry, we learn various sets of rules
for producing graphs of equations.
Given a function p we would
first generate a table of the values of p(x), for
various values of x.
An example table, for 
, follows:
We would then painstakingly plot the points (x,p(x)),
secure in the knowledge that these points satisfy
the equation y = p(x).
We would then draw a line, connecting the points.
Glad to be freed from the tedium of plotting points,
few question the teacher as to why a line connecting
the points may be drawn.
During this lesson,
the teacher with inquisitive students may well be unlucky,
for there is no clear explanation
as to why the connecting line may be drawn.
It turns out that difficulties arise as this method is
applied to general equations.
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