Re: ONE
- From: Martin Wanvik <martinw@xxxxxxxxxxxx>
- Date: Sat, 07 Jan 2006 10:52:05 EST
> You are right about that.
>
> I expressed what I think in a wrong manner.
>
> Let me go back again to the definition of one-one
> relation (
> injection).
>
> f is called one-one mapping from S to P
> if for every x,y belong to S , f(x)=f(y) implies that
> x=y always.
>
> Now how did we knew that x is one member and not two
> members.
>
> for example S={ 1,2,3,4} now 1 belong to S so 1 is
> an element of S.
>
> but also 1,2 belong to S and accordingly 1,2 is an
> element of S.
>
> we should define belonging to S.
>
> For example if belonging to S means anything inside
> the brackets, then
> 1 e S also 1,2 e S also 1,3 e S.
Then your notation is different from what the rest of the world uses. The notation S = {1,2,3,4} usually means that
S is a set containing precicely the _elements_ 1, 2, 3 and 4. There are no other elements, not 1,2 (whatever that means), not the subset {1,2}, or anything else. Anything that is an element is on the list, anything else is not on the list.
You're obviously still confused about the distinction between subset and element, and removing the curly-brackets on the subsets won't help (at least not until you've defined what that means).
> Now so x can be 1 or 2 or 3 or 4 , also x can be 1,2
> or 1,3 or 1,4
> or 2,3 , ...etc, also x can be 1,2,3 or 2,3,4 or
> 1,3,4,..etc
>
> accordingly the definition of one-one relation as
> injection would fail
> these cases.
>
> so what do we mean by the word One.
>
> Zuhair
>
.
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