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Counterexample 52.
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#''The theory of relativity has discontinuities whereby the limit of a physical quantity ...''
 
#''The theory of relativity has discontinuities whereby the limit of a physical quantity ...''
 
#:The formulas connecting momentum, velocity, and mass, are well known, and can be found in any high school or college level textbook on the subject.
 
#:The formulas connecting momentum, velocity, and mass, are well known, and can be found in any high school or college level textbook on the subject.
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#:It is a well-known fact that, by tweaking the order in which various quantities are held constant are allowed to change, one can get different results.  For example, this phenomenon is the essence of the difference between "pointwise continuity" and "uniform continuity" in mathematical analysis.
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#:It is a well-known fact that, by tweaking the order in which various quantities are held constant are allowed to change, one can get different results.  For example, this phenomenon is the essence of the difference between "pointwise continuity" and "uniform continuity" in mathematical analysis, and is the reason why various forms of convergence (pointwise, uniform, and convergence in measure under various <math>L_p</math> norms) in Lebesgue spaces is complicated.
 
#:The formula connecting mass, speed, and momentum is, in all cases without exception:
 
#:The formula connecting mass, speed, and momentum is, in all cases without exception:
 
#:::<math>p^2 (c^2-v^2) =m^2c^2v^2</math>
 
#:::<math>p^2 (c^2-v^2) =m^2c^2v^2</math>
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#:::<math>p = \frac{mcv}{\sqrt{c^2-v^2}}</math>
 
#:::<math>p = \frac{mcv}{\sqrt{c^2-v^2}}</math>
 
#:Note that, expressed in this form, the numerator goes to zero because m goes to zero, and the denominator goes to zero because v goes to c.  This sort of thing is a dead giveaway that some mathematical trickery is going to be invoked.
 
#:Note that, expressed in this form, the numerator goes to zero because m goes to zero, and the denominator goes to zero because v goes to c.  This sort of thing is a dead giveaway that some mathematical trickery is going to be invoked.
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#''Discontinuities in General Relativity are well-recognized.''
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#:The fact that one has found a scholarly paper with the words "discontinuity" and "relativity" in the title does not make relativity false.  It is extremely unlikely that the author of that paper considered relativity to be false; he would surely have used a different title if that were the case.
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#:While only a quick abstract of the paper is given, it appears that the paper is about discontinuities in the ''stress-energy tensor''.  That is completely permissible, and General Relativity can deal with that.
    
Unless someone can come up with a sensible example, we will not be posting further rebuttals.  The recent ones have been hideously pointless, and not worth replying to.  Many of them have cited articles that have ''nothing to do with relativity''.  For example, tides do not disprove relativity.  It's possible that, because of the rather famous nature of the "counterexamples" page (it is cited around the world, and has nearly 2 million web views), people are simply putting in parody, or trolling, or humor, or whatever, in an attempt to see their work on a world-famous page.
 
Unless someone can come up with a sensible example, we will not be posting further rebuttals.  The recent ones have been hideously pointless, and not worth replying to.  Many of them have cited articles that have ''nothing to do with relativity''.  For example, tides do not disprove relativity.  It's possible that, because of the rather famous nature of the "counterexamples" page (it is cited around the world, and has nearly 2 million web views), people are simply putting in parody, or trolling, or humor, or whatever, in an attempt to see their work on a world-famous page.
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