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<div class="moz-cite-prefix">On 2013-08-23 18:52, Gordon wrote:<br>
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<div><span style="font-family: Arial; font-size: 13px;">Adrian
Tymes <a class="moz-txt-link-rfc2396E" href="mailto:atymes@gmail.com"><atymes@gmail.com></a> wrote:</span><br>
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<div>>That last sentence is unclear. What do
you mean by ".999...1"? </div>
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<div>I think it is a fact of mathematics that
.99... carried out to an infinite number of 9s
is equal to 1. No? <br>
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Yes, the symbolic meaning of "0.9999..." corresponds to the real
number 1. It if one of the less well known facts that the number
system we use actually has non-unique number representations. Causes
no end of internet debates.<br>
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<div>If true then when I say "in the limit when I
approach c" it means that in the limit I am
travelling at c. Or at least I don't see the
difference.</div>
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"In the limit" is a bit subtle. It does not mean that "in the limit
of x approaching y" x becomes exactly y, only that x becomes as
close to y as anybody can wish. "1/x goes to infinity in the limit
as a positive x approaches zero" does not mean 1/0 *is* infinity
(especially since stuff goes more and more negative if you approach
from the negative side). <br>
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<pre class="moz-signature" cols="72">--
Dr Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University
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