An uncountable countable set
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From: Han.deBruijn on 23 Sep 2006 14:53 Dik T. Winter wrote: > In article <bf6b$45138cf1$82a1e228$22274(a)news1.tudelft.nl> > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > > > > Mainstream mathematics does not understand what infinitesimals are. > > That is because the recognition of infinitesimals would be suicidal > > to mainstream mathematics and its illusionary "rigour". > > You do not understand either. (Wasn't it Leibniz who has said that he > used them but did not know how to define them, or actually what they > were, and wasn't it Robinson who actually gave a rigorous definition?) Robinson gave a rigorous definition which is completely useless and his *thingies* should not be confused with real infinitesimals, as they are non-rigorously but effectively defined in science and technology. [ ... Dik T. Winter's perpetual and Off-Topic frustration about numerical differentiation deleted ... ] Han de Bruijn
From: Han.deBruijn on 23 Sep 2006 15:22 Dik T. Winter wrote: > If you do not want to hear an answer and just ignore it when it does > not fit in your mind, much effort in responding to you is just wasted. Believe me, Dik, your overall waste of time is really peanuts when compared with mine. Now, do you hear _me_ complaining? You have made your point with that numerical differentiation issue of yours. Everybody can read (Google) what you wrote and draw his/her own conclusions. And maybe you are right and I am wrong. Okay? What else do you want? That I fall on my knees and thank you so much? What fun is it to have a puppet on a string that says "Oh, Dik, how wonderful those numerical differentiations of you are, and soo much more accurate than those I've developed myself". Would you enjoy? Han de Bruijn
From: Virgil on 23 Sep 2006 15:32 In article <1159036717.479525.3060(a)i42g2000cwa.googlegroups.com>, Han.deBruijn(a)DTO.TUDelft.NL wrote: > MoeBlee wrote: > > > Han de Bruijn wrote: > > > to mainstream mathematics and its illusionary "rigour". > > > > The rigor is in a recursive axiomatization with recursive rules of > > inference. You haven't shown that this is an illusion. > > That rigor turns out to be incompatible with useful infinitesimals. Robinson's infinitesimals, and their cousins, are simultaneously useful and rigorous. Whose version of infinitesimals does HdB recommend which are useful but not compatible with rigor?
From: Virgil on 23 Sep 2006 15:37 In article <1159037590.099188.41340(a)m73g2000cwd.googlegroups.com>, Han.deBruijn(a)DTO.TUDelft.NL wrote: > Dik T. Winter wrote: > > > In article <bf6b$45138cf1$82a1e228$22274(a)news1.tudelft.nl> > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > > > > > > Mainstream mathematics does not understand what infinitesimals are. > > > That is because the recognition of infinitesimals would be suicidal > > > to mainstream mathematics and its illusionary "rigour". > > > > You do not understand either. (Wasn't it Leibniz who has said that he > > used them but did not know how to define them, or actually what they > > were, and wasn't it Robinson who actually gave a rigorous definition?) > > Robinson gave a rigorous definition which is completely useless and his > *thingies* should not be confused with real infinitesimals, as they are > non-rigorously but effectively defined in science and technology. HdB conflates true infinitesimals with pseudo-infinitesimals which are merely things which are negligibly small, microscopic, in comparison with macroscopic quantities.
From: Han.deBruijn on 24 Sep 2006 06:14
Virgil wrote: > In article <1159037590.099188.41340(a)m73g2000cwd.googlegroups.com>, > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > > Dik T. Winter wrote: > > > > > In article <bf6b$45138cf1$82a1e228$22274(a)news1.tudelft.nl> > > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > > > > > > > > Mainstream mathematics does not understand what infinitesimals are. > > > > That is because the recognition of infinitesimals would be suicidal > > > > to mainstream mathematics and its illusionary "rigour". > > > > > > You do not understand either. (Wasn't it Leibniz who has said that he > > > used them but did not know how to define them, or actually what they > > > were, and wasn't it Robinson who actually gave a rigorous definition?) > > > > Robinson gave a rigorous definition which is completely useless and his > > *thingies* should not be confused with real infinitesimals, as they are > > non-rigorously but effectively defined in science and technology. > > HdB conflates true infinitesimals with pseudo-infinitesimals which are > merely things which are negligibly small, microscopic, in comparison > with macroscopic quantities. Hey! Virgil clearly _has_ a clue about real world infinitesimals. Han de Bruijn |