What makes a trivial operator trivial ?
in [Math]
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From: Androcles on 31 Jan 2010 11:12 "Aage Andersen" <aaan(REMOVE)@email.dk> wrote in message news:4b65a3d1$0$56792$edfadb0f(a)dtext02.news.tele.dk... > > "Huang" >> Zero apples is the same thing as zero oranges. It is nonsense to say >> that apples are oranges, except in such trivial instances as this. If >> zero was the only number you had at your disposal, all you would be >> able to do is trivial and/or nonsensical procedures. > > I think it is a mistake to consider zero apples the same as zero oranges. > Evidently you do not think.
From: J. Clarke on 31 Jan 2010 12:53 Huang wrote: > On Jan 31, 9:38 am, "Aage Andersen" <aaan(REMOVE)@email.dk> wrote: >> "Huang" >> >>> Zero apples is the same thing as zero oranges. It is nonsense to say >>> that apples are oranges, except in such trivial instances as this. >>> If zero was the only number you had at your disposal, all you would >>> be able to do is trivial and/or nonsensical procedures. >> >> I think it is a mistake to consider zero apples the same as zero >> oranges. >> >> Aage > > > They may be regarded as being identical, or non-identical. I think it > gets into the area of proveability, but also seems intrinsically > indeterminate. So indeterminacy seems to be related to these extremely > simplistic things. And once again we see that you have to define your sets before you attempt to argue their properties. We can represent a condition of being devoid of oranges by {0 oranges} or by the empty set {}, or no doubt by some other means. {0 oranges} is not {} nor is it {0 apples}. In practical terms it makes a difference whether it's the apple barrel or the orange barrel that is empty--getting that wrong when you reorder means that you're overstocked with one and remain devoid of the other.
From: Sam Wormley on 31 Jan 2010 14:50 One that says, "One ringy-dingy, two ringy-dingy, ... ".
From: Bacle on 31 Jan 2010 11:26 > > "Aage Andersen" <aaan(REMOVE)@email.dk> wrote in > message > news:4b65a3d1$0$56792$edfadb0f(a)dtext02.news.tele.dk... > > > > "Huang" > >> Zero apples is the same thing as zero oranges. It > is nonsense to say > >> that apples are oranges, except in such trivial > instances as this. If > >> zero was the only number you had at your disposal, > all you would be > >> able to do is trivial and/or nonsensical > procedures. > > > > I think it is a mistake to consider zero apples the > same as zero oranges. > > > Evidently you do not think. Not so, if he meant this: if one is to consider zero apples (or a collection with zero apples) as an empty set of apples, same for oranges. Then we cannot say that the empty set of apples is the same as the empty set of oranges, as there can be only one empty set (if not, one empty set E contains an element not contained in an empty set E' ...) > > > > >
From: Huang on 1 Feb 2010 00:02
On Jan 31, 10:18 am, "Aage Andersen" <aaan(REMOVE)@email.dk> wrote: > "Huang" > > "Aage Andersen" > > > "Huang" > > > > Zero apples is the same thing as zero oranges. It is nonsense to say > > > that apples are oranges, except in such trivial instances as this. If > > > zero was the only number you had at your disposal, all you would be > > > able to do is trivial and/or nonsensical procedures. > > > I think it is a mistake to consider zero apples the same as zero oranges. > > They may be regarded as being identical, or non-identical. I think it > gets into the area of proveability, but also seems intrinsically > indeterminate. So indeterminacy seems to be related to these extremely > simplistic things. > > -------------------------------------------- > > -2 oranges /= -2 apples > -1 oranges /= -1 apples > 0 oranges ?= 0 apples > 1 oranges /= 1 apples > 2 oranges /= 2 apples > > in general n oranges /= n apples, if n /= 0 > > Why this discontinuity for n = 0? > > I prefer 0 oranges /= 0 apples. > > Perhaps we could DEFINE: 0 oranges /= 0 apples ? > > Aage You could approach this by carefully trying to define things to contain the issue. Or, you could simply adopt a new philosophical view and call this an example of anti-uniqueness. Invent it as a new phenomena and give it a name. |