Irrational Square Roots
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From: Bart Goddard on 7 Aug 2010 23:50 Counterclockwise <snowmenofdoom(a)gmail.com> wrote in news:672114959.74230.1281234324264.JavaMail.root(a)gallium.mathforum.org: > Oh, you're right. I did a quick read through, I forgot exactly what it > was by the end of it. > > As far as OP's finite decimal is concerned, a simple reversal will fix > that. "A number that has no representation with only 0's after the > decimal" > So now 3.14 is not a finite decimal. This is getting _hard_. -- Cheerfully resisting change since 1959.
From: Bart Goddard on 7 Aug 2010 23:54 Counterclockwise <snowmenofdoom(a)gmail.com> wrote in news:129182689.74114.1281231440967.JavaMail.root(a)gallium.mathforum.org: > Every definition is deficient on some level. That's not the problem here. > In this case, perhaps a fitting definition would be, "A number that > could be represented without the use of a decimal point", or more > precisely again, "A number that only has 0's after the decimal". It's not that the definition is "deficient", but that's it's wrong. Pi can be represented without a decimal, by just writing "pi". And, again, 3.9999..... doesn't have only 0's after the decimal. -- Cheerfully resisting change since 1959.
From: Bart Goddard on 7 Aug 2010 23:56 Counterclockwise <snowmenofdoom(a)gmail.com> wrote in news:1506819726.74129.1281231947918.JavaMail.root(a)gallium.mathforum.org: > Or, taking in mind the earlier ribbing about 0.99999999, "A number > that can be represented with only 0's after the decimal" > > Really, I could do this all night and keep coming up with new reasons > why the definition isn't precise enough. > You could "this" all night, but what you are doing isn't showing deficiencies in this or that definition. The MathWorld definition is just fine. The only difficulty with it is various folks' inability to comprehend it. OTOH, the proffered alternates aren't just deficient, they're ambiguous, if not self-contradictory. -- Cheerfully resisting change since 1959.
From: Arturo Magidin on 8 Aug 2010 00:10 On Aug 7, 9:24 pm, Counterclockwise <snowmenofd...(a)gmail.com> wrote: > Oh, you're right. I did a quick read through, I forgot exactly what it was by the end of it. Is it any surprise then that your opinions and suggestions were worthless? > As far as OP's finite decimal is concerned, a simple reversal will fix that. > "A number that has no representation with only 0's after the decimal" Really? That's the definition of "finite decimal" that you are looking for? Perhaps in addition to quick readthroughs you also do quick thinkthroughs. You might want to pause and reflect next time. -- ArturO Magidin
From: Gerry on 8 Aug 2010 02:37
On Aug 8, 11:00 am, Bill Dubuque <w...(a)nestle.csail.mit.edu> wrote: > Gerry <ge...(a)math.mq.edu.au> wrote: > >Gerry Myerson <ge...(a)maths.mq.edi.ai.i2u4email> wrote: > > >> No. But with guys like Archimedes and Diophantus and Eudoxus > >> and Euclid all hanging around, I'm confident that someone > >> figured it out back then. > > [...] > > Not to mention an error in the use of the apostrophe > > that should be obvious even to a beginning English student. > > Did he really put "It's" in the title of his book, when > > it should have been "Its"? > > Gerry: your prior two posts in this thread seem to indicate > that you do not always take historical matters very seriously. > Should that change I'll be happy to continue the discussion, > just as we did last time around on closely related historical > topics (Estermann's irrationality proof [1]). Bill, I've made 11 posts to this thread (not counting this one), so perhaps you do not always take arithmetical matters very seriously. I will admit that the things you do take seriously you take far more seriously than I do. In any event, my feeling is this: if you had gone up to Euclid and asked him, in terms that would have made sense to him, whether the square root of 101 is rational, he would have been able to answer the question without hesitation and he would have been able to provide you with a proof of (what we would call) the irrationality. I can't cite any documentation for this feeling, so you would be justified in remarking that I am not being serious, but let me ask you: do you think my feeling is wrong? -- GM |