Am Montag, 27. Oktober 2008 11:46 schrieb Henning Thielemann:
On Mon, 27 Oct 2008, Janis Voigtlaender wrote:
Henning Thielemann wrote:
I think one reason is that repeated rounding should not be worse than rounding in one go. Consider the rule 'use ceiling when the first removed digit is 5'. Then
0.45 - (round to one place) -> 0.5 - (round to integer) -> 1
But repeated rounding *is* worse than rounding in one go, under any reasonable scheme:
3.46 -> 3.5 -> 4
With the rounding-to-even route this would be
3.46 -> 3.4 -> 3
Wait, that cannot be. 6 > 5, so 3.46 -> 3.5 even with banker's rounding.
so rounding in passes is no worse than rounding in one go for this example.
Rounding in passes is bad per se, because there are pretty large intervals where that gives a different result from a direct rounding.
vs.
3.46 -> 3
That was actually the debate with that teacher. Unbelievable as that still is to me today, she advocated the 3.46 -> 3.5 -> 4 route ...
I also know a didact which tells teachers that 1 has no prime decomposition. Oh, I see, she may have copied that from Wikipedia: http://en.wikipedia.org/wiki/Prime_factorisation
I can believe that makes sense to somebody who considers 0 an unnatural number, an empty product must be frightening for them.