Does inductive reasoning lead to knowledge?
in [Logic]
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From: Tim Golden BandTech.com on 20 Jan 2010 22:04 On Jan 20, 8:00 pm, Marshall <marshall.spi...(a)gmail.com> wrote: > On Jan 20, 3:25 pm, "Tim Golden BandTech.com" <tttppp...(a)yahoo.com> > wrote: > > > > > Regardless of how many zeros you'd like to enforce you'll still have a > > term > > b i > > which is a product and which is inconsistent with the closure > > requirement of the ring product because b is real and i is not real. > > You are hallucinating: b is complex. You also are apparently Here I take the opportunity to falsify your statement above. b is not complex. b is real. Please falsify my own statements in such a direct manner and you will have something. - Tim > unable to specify which ring, and hence which ring product, > you are talking about. > > > The zeros are quite > > meaningless. We can throw zeros in anywhere anytime we like so long as > > they are superposed (summed). To rely upon these zeros for any > > argument is a weak stance. I did not offend your requirement that b > > carry a zero. I built a b' and it need not carry that requirement. The > > requirement is pure silliness based on the logic of zeros which starts > > this paragraph. I'll stand by my own falsification of your statement > > on uniqueness, since you've allowed the additional components by > > stipulating additional components for your construction. > > That's hilarious! You misread the original statement as calling > for unique reals; you also claim that you can construct some > other number b' that doesn't meet the requirements given; > yet you still "stand by" your position. > > > The closure principle makes such a simple discrepancy of such > > constructions yet noone bothers to criticize except me as far as I can > > tell. > > Indeed you are the only one who sees a problem. The obvious > conclusion is that everyone else is blind and only you can > see the truth. > > http://en.wikipedia.org/wiki/Crank_%28person%29 > > > Shall I just declare a hoax and reboot the matrix? Are we all > > just apes anyway? Seems like proof to me. I await falsification of my > > statements. > > They were false when you first wrote them. The distinctions > necessary for *you* to see how false they are are apparently > not distinctions you are capable of making: specifically, the > distinction between the product of the real ring and of the > complex ring. > > Marshall
From: Marshall on 20 Jan 2010 22:24 On Jan 20, 7:04 pm, "Tim Golden BandTech.com" <tttppp...(a)yahoo.com> wrote: > On Jan 20, 8:00 pm, Marshall <marshall.spi...(a)gmail.com> wrote: > > > On Jan 20, 3:25 pm, "Tim Golden BandTech.com" <tttppp...(a)yahoo.com> > > wrote: > > > > Regardless of how many zeros you'd like to enforce you'll still have a > > > term > > > b i > > > which is a product and which is inconsistent with the closure > > > requirement of the ring product because b is real and i is not real. > > > You are hallucinating: b is complex. You also are apparently > > Here I take the opportunity to falsify your statement above. > b is not complex. b is real. > Please falsify my own statements in such a direct manner and you will > have something. You're on: There does not exist a number that is a member of the set of real numbers that is not also a member of the set of complex numbers. Marshall
From: jbriggs444 on 21 Jan 2010 08:33 On Jan 20, 10:24 pm, Marshall <marshall.spi...(a)gmail.com> wrote: [...] > You're on: > > There does not exist a number that is a member of > the set of real numbers that is not also a member of the > set of complex numbers. You've overstated the case significantly here. _IF_ we define the complex numbers as ordered pairs of reals under the obvious cartesian coordinate method _THEN_ there is no real number that _is_ also a complex number. [My background is real analysis. This is the obvious construction] _IF_ we define the complex numbers as the closure of the real numbers plus i under the obvious rules for how addition and multiplication treat imaginary numbers _THEN_ there is no real number that _is not_ also a complex number. [I've never been exposed to the foundations of the complex numbers from an algebraic point of view, but I expect that this is the kind of basis you might want to put under them] _IF_ we define the "foobar numbers" as ordered pairs of reals under the obvious cartesian coordinate method and then define the "complex numbers" as the isomorphic set produced by replacing each (x,0) pair in the "foobar numbers" with the real number x _THEN there is no real number that _is not_ also a complex number. [This is the obvious foundation an analyst could put under the complex numbers if somebody wants to get bitchy about subnet relations] To an analyst, all three statements are obviously true. (*) And the distinction is irrelevant. Whether there is a sub-ring of the complex numbers that _is_ the real numbers or whether the sub-ring is merely isomorphic to the real numbers is of little consequence. I was trained as a Dedekind cut guy. But I feel no need to declare Jihad against the infidel Cauchy sequence dudes.
From: Aatu Koskensilta on 21 Jan 2010 08:42 jbriggs444 <jbriggs444(a)gmail.com> writes: > I was trained as a Dedekind cut guy. But I feel no need to declare > Jihad against the infidel Cauchy sequence dudes. Well, yes. Such matters turn on but uninteresting (from a general mathematical point of view) details of the set theoretic construction adopted, and are of no wider mathematical significance whatever. That a real number is a complex number is a wholly unobjectionable claim in ordinary mathematics. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: J. Clarke on 21 Jan 2010 09:45
Aatu Koskensilta wrote: > jbriggs444 <jbriggs444(a)gmail.com> writes: > >> I was trained as a Dedekind cut guy. But I feel no need to declare >> Jihad against the infidel Cauchy sequence dudes. > > Well, yes. Such matters turn on but uninteresting (from a general > mathematical point of view) details of the set theoretic construction > adopted, and are of no wider mathematical significance whatever. That > a real number is a complex number is a wholly unobjectionable claim in > ordinary mathematics. I think it really gets down to the oft-discussed concept of "mathematical maturity". |