From: PointedEars@web.de   
      
   Ross Finlayson wrote:   
   > On 12/10/2025 06:20 PM, Thomas 'PointedEars' Lahn wrote:   
   >> Ross Finlayson wrote:   
   >>> On 12/09/2025 02:47 PM, Thomas 'PointedEars' Lahn wrote:   
   >>>> Ross Finlayson wrote:   
   >>>>> For example, in relativity theory, a material point's   
   >>>>                     ^^^^^^^^^^           ^^^^^^^^^^^^^^   
   >>>>> absolute motion with regards to its own frame is   
   >>>>     ^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^   
   >>>>   
   >>>> ... a sentence containing multiple contradictions in terms.   
   >>>>   
   >>>> As is *evident* here, too, you have no clue what you are talking about.   
   >>>   
   >>> No, rather _contradistinctions_ in terms.   
   >>   
   >> Another word that you just made up, and only you know the meaning of.   
   >>   
   >> Does this make you *feel* smarter than everybody else?   
   >   
   > https://en.wikipedia.org/wiki/Dictionary   
   >   
   > https://en.wiktionary.org/wiki/contradistinction   
      
   Granted.  But unsurprisingly, you are not using that word correctly.  The   
   confused nonsense that you had written has nothing to do with what it means.   
      
   In particular: The _theories_ of *relativity* are precisely about that   
   _there is no absolute motion_.  However, an object is _at rest_ in its   
   *own frame* *by definition*: that is what "own frame" *means*; it is   
   short for "its (own) *rest* frame".   
      
   > Consider for example the geometric series for   
   > the inverse powers of two,   
   >   
   > 1/2 + 1/4 + ...   
   >   
   > vis-a-vis 1 minus that   
   >   
   > 1 - 1/2 - 1/4 - ...   
   >   
   > and the _contradistinction_ of 0 and 1,   
   > _only defined by not being each other_.   
      
   False.  0 is defined as the neutral element of addition: If (F, +, ⋅) is a   
   field, then   
      
     ∀ a ∈ F: ∃ 0 ∈ F: 0 + a = a + 0 = a.   
      
     [It turns out that 0 is unique in the field.  Let 0* be another element   
      of the field that satisfies the one-condition, then   
      
         ∀ a ∈ F: 0* + a = (0* + 0) + a = 0 + a  ==>  0* = 0.]   
      
   1 is defined as the neutral element of multiplication: If (F, +, ⋅) is a   
   field,   
      
     ∀ a ∈ F: ∃ 1 ∈ F: 1 ⋅ a = a ⋅ 1 = a.   
      
     [It turns out that 1 is unique in the field.  Let 1* be another element   
      that satisfies the one-condition, then   
      
         ∀ a ∈ F: 1* ⋅ a = (1* ⋅ 1) ⋅ a = 1 ⋅ a  ==>  1* = 1.]   
      
   > So, the limits of these series exist, and are 1 and 0 respectively,   
      
   Yes.   
      
     1/2 + 1/4 + ...   
     = ∑_{k=1}^∞ 1/2^k   
     = ∑_{k=1}^∞ (1/2)^k   
     = [∑_{k=0}^∞ (1/2)^k] - 1   
     = 1/[1 - 1/2] - 1   
     = 1/[1/2] - 1   
     = 2 - 1   
     = 1.   
      
     1 - 1/2 - 1/4 - ... = 1 - (1/2 + 1/4 + ...) = 1 - 1 = 0.   
      
   > yet, according to induction, no initial segment is the limit.   
      
   I do not see your point.   
      
   > I'm a pretty smart guy, ..., [...]   
      
   Notice that I never asked you whether you *would* be smarter.  So thanks for   
   confirming unambiguously that you are suffering from delusions of grandeur.   
      
   --   
   PointedEars   
      
   Twitter: @PointedEars2   
   Please do not cc me. / Bitte keine Kopien per E-Mail.   
      
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