Welcome to online math tutors,
This is a great
opportunity to explore how math is done on help with math problems,
at a basic level. The problem
you have, of course, is that the concept of "opposite" is so "obvious"
that mathematicians, as far as I can see, don't bother to state the
definition they all assume is well known. That gives you a chance to
work out a "new" definition as if you were on the cutting edge of
math.
How do we define a mathematical concept? Generally, we start with
common sense, then make it mathematical by turning that into a precise
and general definition. In this case, "opposite" is a natural concept
if we start by looking at a circle. In fact in free math, any definition we choose
will identify the same point as opposite a given point: halfway around
the circumference; having a parallel tangent; at the other end of a
diameter, which divides the interior into equal halves; or whatever
you want to say.
This is a great
opportunity to explore how math is done on help with math problems,
at a basic level. The problem
you have, of course, is that the concept of "opposite" is so "obvious"
that mathematicians, as far as I can see, don't bother to state the
definition they all assume is well known. That gives you a chance to
work out a "new" definition as if you were on the cutting edge of
math.
How do we define a mathematical concept? Generally, we start with
common sense, then make it mathematical by turning that into a precise
and general definition. In this case, "opposite" is a natural concept
if we start by looking at a circle. In fact in free math, any definition we choose
will identify the same point as opposite a given point: halfway around
the circumference; having a parallel tangent; at the other end of a
diameter, which divides the interior into equal halves; or whatever
you want to say.
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