On Sun, Mar 9, 2014 at 12:58 PM, Mark H. Harris email@example.com wrote:
hi Steven, that's a straw man. Your argument presumes that False is a surprise. I am not in the least surprised. As, I am also not surprised by this:
dscale(32) 10100 d(1)/3 Decimal('0.33333333333333333333333333333333') <=== not a surprise, expected d(1)/3 + d(1)/3 +d(1)/3 Decimal('0.99999999999999999999999999999999') <=== not a surprise either, quite expected
I was trying to construct a proof from memory that would support this case, but I got tangled, so I cheated and went to Wikipedia for something similar.
Let's start with two variables, a and b, which we shall suppose are equal.
# Postulation? Or is this called an axiom? I don't remember.
a = b
# Wave hands vigorously and conclude that:
a = 0
Are you surprised? Probably. Normally, two variables being equal doesn't prove the value of either. Without knowing what actual handwaving went on in there, that is and should be a surprising result. Now, here's the handwaving, spelled out in full:
# As above, start here
a = b
# Multiply both sides by a
aa = ba
# Subtract bb (aka b squared, ASCII-friendly) from both sides
aa - bb = ba - bb
# Factor (both sides separately)
(a + b) (a - b) = b (a - b)
# Cancel out the multiplication by (a - b)
a + b = b
# Subtract b from both sides
a = 0
And there you are. To be unsurprised by the result, you have to know exactly what happened in between, and how it's different from the conventional rules of mathematics. Someone who already understands all that may well not be surprised, but someone who's expecting sane real-number arithmetic is in for a shock.