Galileo's Paradox
in [Math]
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From: Virgil on 6 Dec 2006 14:41 In article <4576E6E7.1010404(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/5/2006 11:27 PM, Virgil wrote: > > In article <1165333562.354313.109050(a)j44g2000cwa.googlegroups.com>, > > "Tonico" <Tonicopm(a)yahoo.com> wrote: > > > >> Eckard Blumschein ha escrito: > >> > >> > On 12/4/2006 11:52 PM, Virgil wrote: > >> > > >> > >> I am an electrical engineer > >> > > > >> > > Shocking! > >> > > >> > Why? We love mathematics. > >> *************************************************** > >> Oh, I bet elec. eng. love maths; the problem seems to be that maths > >> does not correspond AT ALL that love, at least in the case of several > >> engineers...**sigh**...tough. > >> Tonio > > > > Electrical stuff can be shocking to those who use it carelessly or abuse > > it, > > Do you refer to the electric chair? Is that what your engineering expertise has been engaged in designing?
From: Virgil on 6 Dec 2006 14:43 In article <4576E9AC.2020006(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/5/2006 11:36 PM, Virgil wrote: > > >> One has to be pretty miseducated in order to need the fancy aleph_1. > > > > That depends on whether one accepts or rejects the continuum hypothesis. > > Not at all. EB again demonstrates that mathematically he does not know what he is talking about
From: Virgil on 6 Dec 2006 14:48 In article <4576EB55.4040803(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/5/2006 11:41 PM, Virgil wrote: > > In article <457593EB.9030809(a)et.uni-magdeburg.de>, > > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > > >> > >> Rationals are p/q. This system cannot be improved by adding genuine > >> (i.e. rational) numbers. One can merely move to the fictitious > >> continuous alternative. > > > > All numbers are equally genuine in any meaning of "genuine" other than > > EB's improper meaning of "irrational". > > Kronecker was correct in that irrationals are no geunine numbers. That may have been thought to be the case in the ninteenth century, but this is the twenty first century. Kronecker died in 1891. Mathematics has progressed since then.
From: Virgil on 6 Dec 2006 14:52 In article <4576EDC6.6090307(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/5/2006 11:48 PM, Virgil wrote: > > In article <457596BC.3040307(a)et.uni-magdeburg.de>, > > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > > >> On 12/4/2006 10:47 PM, David Marcus wrote: > > > >> >> Standard mathematics may lack solid fundamentals. At least it is > >> >> understandable to me. > >> > > >> > If it is understandable to you, then convince us you understand it: > >> > Please tell us the standard definitions of "countable" and > >> > "uncountable". > >> > >> I do not like such unnecessary examination. > > > > Then stop trying to examine others. > > I examined others here? You try, but as you are proceeding from a false assumption: that your own understanding of mathematics is superior to that of thousands of others who have spent much more time and effort and talent in gaining their understanding than you have.
From: Virgil on 6 Dec 2006 14:54
In article <4576EED0.5070804(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/5/2006 11:50 PM, Virgil wrote: > > In article <45759AD4.3040505(a)et.uni-magdeburg.de>, > > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > > >> On 12/4/2006 9:58 PM, Bob Kolker wrote: > >> > Eckard Blumschein wrote: > >> > > >> >> No wonder. Exactly this selfdelusion was the intention of dedekind. > >> > > >> > 'Twas no delusion. > >> > > >> > The Dedikind cut defining the square root of 2 is just as well defined > >> > as the successor to the integer 2. > >> > > >> > Bob Kolker > >> > >> Dedekind's cuts did not create any new number. The square root of two is > >> still what it was before. > > > > The cuts provided a construction of sets having the properties of those > > numbers, i.e., a model of the reals within set theory. > > They supported the illusion that there are genuine numbers which > complete the rational ones. Actually there are merely indirect > definitions of irrational positions between the rationals. Indirect is sufficient for existence in the mathematical sense, so that EB has conceded that reals exist. |