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) - Re: Hello There?
... >A sequence of 2 decimal digits could represent any value, ... So in the infinite decimal expansion ... Prev by Date: ...
(sci.logic) - 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. ...
(borland.public.delphi.non-technical) - 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: ...
(borland.public.delphi.non-technical) |
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