pka
Elite Member
- Joined
- Jan 29, 2005
- Messages
- 11,971
Hello Mates, There is no infinite summation in reply #35.I don't understand what you are saying
I think you are thinking about a sum like [imath]\sum\limits_{n-1}^{\infty}[9\cdot10^{-n}]=0.9+0.09+0.009+\cdots=1[/imath] SEE HERE
Now once again that is a limit of sum. It is one number.
[imath]0.9+0.09=0.99[/imath] is one number. [imath]0.9+0.09+0.009+\cdots[/imath] is not one number.
Of course, the representation [imath]0.\overline{\,9\,}=1[/imath] is shorthand and is one number, but not what you asked about.
On the subject of notation, the cardinality of a set is usually denoted by [imath]|A|[/imath]
However alternatively maybe denoted by [imath]n(A),~\|A\|,~\text{card}(A),~\overline{\,A\,}[/imath] among others.
Be careful of that last one because almost universally it is used for the negation of [imath]A[/imath].