Re: Problems I have with 1.999...=2

In article <lZ9ge.12093$U01.10469@trnddc07>,
Kirby Cook <kwmcook@xxxxxxxxxxx> wrote:

>The assertion that the sum is infinite means, to me, that there is no
>point where it will equal 1 and be, therefore, finished, and finite.

No.

The term "infinite sum" is shorthand for "the limit of the infinite
sequence of partial sums". The infinite sequence is indeed never
finished, but the infinite sum is not the infinite sequence, it is the
limit of it, which in this case is 1.

As far as I am aware, 1 has been finished and finite for some time now.

-- Richard
.

Relevant Pages

  • Re: infinity
    ... > were inconsistent, then it is only because ZF itself is inconsistent. ... There are minimal extensions to ZFC which do deal ... >>> No, ZF is inconsistent, and infinite sets are equivalent. ... > We can perform this sum only thanks to Countable Additivity. ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... the sum of a countable number of 0's; he simply "wants" it to be 1. ... then the probability of one being chosen is 1. ... the question is why the standard system can't accomodate the infinite case, ... The probability of each is 0 in standard analysis, ...
    (sci.math)
  • Re: An uncountable countable set
    ... All the numbers on the right are finite, so the sum must ... Apparently a sum can only be infinite if one of the ... restricting the string ... enumerating the naturals using increment to generate the next successor. ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... therefore there must exist a uniform distribution on the naturals. ... If you use a 2 element set, you still get a total probability of 1. ... the sum of a countable number of 0's; he simply "wants" it to be 1. ... the question is why the standard system can't accomodate the infinite case, ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... If one of the elements is to be chosen from the set, then the probability of one being chosen is 1. ... then that 1 representing the fact that one of those will be chosen is defined to be the sum of the probabilities of each. ... the question is why the standard system can't accomodate the infinite case, with an infinite number of equally likely outcomes, one of which will definitely happen. ...
    (sci.math)