Re: Idle Thoughts

Henrick,

No. You might be confusing the concept of a sequence with the concept of a series. The /sequence/ is the numbers 0.9, 0.99, 0.999,...etc in order. Each number in this sequence can be expressed as a /series/ on the form num(n) = (sum of 9/(10 to the power of k) where k = 1 to n). The expression 0.9(bar) is short hand for a number with an infinite decimal expansion. This number is *not* part of the sequence of which 1 is the limit. The sequence contains numbers with a finite number of decimals only. Instead, the expression 0.999999... is, in turn, short hand for the limit of the previously mentioned sequence of finite series. 

indeed. i don't think it's possible to explain this any more clearly...
.

Relevant Pages

  • Re: Idle Thoughts
    ... finite series in the sequence approach 1/3 even closer. ... The expression 0.9is short hand for a number with an infinite decimal expansion. ... is, in turn, short hand for the limit of the previously mentioned sequence of finite series. ...
    (borland.public.delphi.non-technical)
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  • Re: Idle Thoughts
    ... It is an infinite series approaching 1/3 ever closer. ... (BTW none of the finite series in the sequence is infinite. ... mathematicians are reluctant to speak of "infinite series" since what they really talk about are limits of sequences of growing finite sequences. ...
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  • Re: Idle Thoughts
    ... It is the limit of a sequence of finite series. ... > finite series in the sequence approach 1/3 even closer. ... Prev by Date: ...
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