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Article #927Re: 100% =/= 99.99...%
From: Wén Shào
Date: Wed, 07 Sep 2011 05:15
Date: Wed, 07 Sep 2011 05:15
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2727 bytes
On Thursday, April 7, 2011 2:18:36 PM UTC+10, Graham Cooper wrote: > I coined a phrase just now... > > I am 99.99.... recurring % certain that Proposition A is true! > > Now it occurs to me that should Proposition A turn out to be false, I > have some room to manouver by claiming there was 1 chance in Infinite > possibilites that Proposition A was false, so that's why I wasn't 100% > certain! > > That would have a good chance of holding up in a court of law, but a > claim with a 100% certainty guarantee which was proven false, would > clearly not stand up in court! > > So, as a matter of notation, 0.99... could refer to the non > terminating expansion and 1 could refer to the limit of that at > infinity! > > Since 1/X never reaches 0, 1/X as X->oo is not zero, it merely > approaches it! > The claim that 1 over X as X tends to infinity is not zero is not true. I understand your claim, you are saying for any fixed(of course finite) X, 1/X is just a very small positive number, strictly larger than 0. But mathematically, we use limit 1/x = 0 when x tends to infinity to describe a dynamic process. In another word, you can regard 1/x as zero if x can be made arbitrarily large. Just my thought
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From: Wén Shào <90b5.6587@gmail.com>
Newsgroups: aus.science
Subject: Re: 100% =/= 99.99...%
Date: Tue, 6 Sep 2011 22:15:12 -0700 (PDT)
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