Our disagreement seems to derive from my use of the words “different flawed step” and your use of “same flaw”. Eliezer suggested substituting 1 for x and y in :
(x+y)(x-y) = y(x-y)
x+y = y
yielding
(1+1)(1-1) = 1(1-1) (true)
1+1 = 1 (false)
Thus, since a true equation was transformed into a false one, the step must have been flawed.
Under my suggestion, we have:
(0+0)(0-0) = 0(0-0) (true)
0+0 = 0 (true)
So, under Eliezer’s suggested criterion (turning true to false) this is not a flawed step, though if you look carefully enough, you can still notice the flaw—a division by zero.
So, under Eliezer’s suggested criterion (turning true to false) this is not a flawed step, though if you look carefully enough, you can still notice the flaw—a division by zero.
Hmm. A failure to identify a flawed step doesn’t mean that the step isn’t flawed.
A true statement turning into a false one does show that you manipulated it badly—but a true statement staying true doesn’t show that you manipulated it well.
Actually, x=y=0 still catches the same flaw, it just catches another one at the same time.
Our disagreement seems to derive from my use of the words “different flawed step” and your use of “same flaw”. Eliezer suggested substituting 1 for x and y in :
yielding
Thus, since a true equation was transformed into a false one, the step must have been flawed.
Under my suggestion, we have:
So, under Eliezer’s suggested criterion (turning true to false) this is not a flawed step, though if you look carefully enough, you can still notice the flaw—a division by zero.
Hmm. A failure to identify a flawed step doesn’t mean that the step isn’t flawed.
A true statement turning into a false one does show that you manipulated it badly—but a true statement staying true doesn’t show that you manipulated it well.