A while ago, one of the folks on this list remarked on the amount
of time he had to spend teaching remedial math. He said that some
of his students were not sure whether (x minus x) was equal to zero.
I'm not sure what is the best way to handle it. The following
is almost certainly NOT the right way:
Q: Are you sure that x minus x is zero?
A: Pretty sure. It's zero by definition.
Q: Huh? Is that the definition of zero?
A: It's the definition of "minus". Additive inverse.
I am reminded of the proverb that says
Learning proceeds from the known to the unknown.
The problem here is that the students may never have known the
definition of "zero" and "minus" ... or if they did, they have
long since forgotten.
So at this point the teacher has to wonder, where are the students
coming from? What could possibly lead them to think that x minus
x could be anything other than zero?
The obvious culprit is sig figs. If you measure x=2.54 and y=2.54
and subtract them, the difference is not necessarily zero. This
is a disaster. The sig figs method teaches people to subtract
things that evidently are not numbers, because they do not uphold
the laws of arithmetic. They do not uphold the axioms that define
what we mean by "zero" and "minus" and "number".
This is reason #452 why nobody in the real world uses sig figs.
Earlier this week I got a call from a physics professor. Her kid
is just starting physics class, in a high school in a college town.
They spent the first several days covering sig figs.
-- The kid asks the mom, what the heck is this?
-- The mom asks me, what the heck is this? When I was in high
school, we did real physics, not this garbage.
-- What am I supposed to say? It's not nice to tell the kid
to ignore everything the teacher says.
Please folks: Every minute spent on sig figs is at least two
minutes wasted, because it will all have to be unlearned. Skip
it and do some real physics instead.