Is 0 the same thing as infiniti?

[derekmcd]

There was a recent thread in phenomena concerning this very topic and vanDivX summed it up quite nicely with this post. <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

 

[vandivx]

thx <img src="/images/icons/laugh.gif" /><br />I am mighty pleased that somebody sides with me (even if it might be only partly for all I know) as your pointing out that thread implies, it always seems like one is against the whole world and nobody agrees at all with what one says<br /><br />but there is always something to add or expand upon especially since one always gets feeling the message is not getting accross<br /><br />strictly speaking zero is not a number, numbers are 1,2,3,... that's also the reason why it was invented only later on after numbers have been long in use - and since I have argued in that post that infinity is not a number either, it might be viewed that zero and infinity have that in common but that is a relationship that has no usefull message in it for the audience so to speak<br /><br />if anything infinity is best compared to the infinitesimal, the name alone would lead one to suspect that they are very similar if not the same, their function in mathematics is the same in principle and they differ only in that one caps the number series at the upper end and the other at the lower end<br /><br />one might see zero as the lower end of number series but zero fails us when we take into account fractions of numbers and try to specify the smallest one - zero is not a fraction and has no 'size' and won't do for this purpose<br /><br />when it comes to 'smallest something' as opposed to nothing we have to invent infinitesimal which is itself not a fraction (similar to infinity not being a number) but a limit of fractions with precisely defined ways how it is handled (again similar to infinity which also has its specific ways how it should be used)<br /><br />just like infinity is bigger than any number by definition so the infinitesimal is smaller than any fraction of a number - again by definition, both were invented to function as caps of number series because at the upper end the series is open ended and at the lower end the zero is not a cap for the purp <div class="Discussion_UserSignature"> </div>

 

[derekmcd]

Just because I'm not looking at ya doesn't mean I'm not paying attention <img src="/images/icons/smile.gif" />. <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

 

[yevaud]

Of course, on a simple number line, the difference becomes grossly apparent.<br /><br />Zero is a definable "place." Infinity is beyond asymptotic; it is forever unachievable.<br /><br />(Just thought I'd throw that in to screw things up. <img src="/images/icons/wink.gif" /> ) <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[derekmcd]

Infinity in it's raw definition is something 'unachievable' or 'unviewable'... 'undefinable' (insert random description here). When considering mathematics, it is simply a <b>limit</b>.<br /><br />Most folks ascribe inifinity as a numerical concept; however, I agree with vanDivX that the concept of infinity is really nothing more than a 'upper end' limit to our though process. <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>

 

[vandivx]

"Zero is a definable "place." Infinity is beyond asymptotic; it is forever unachievable."<br />---<br /><br />and same for the infinitesimal, it is also forever unachievable, worse than chasing your tail <img src="/images/icons/smile.gif" /><br /><br />in that way the infinity is conceptually the same as the infinitesimal except they are exact opposites<br /><br />both are abstract tools of mathematics and have no physical meaning in the real world, on the other hand if they were finite and so had that meaning then they would loose the utility they have in mathematics (they would become just another number and we already have lots of those LOL)<br /><br />vanDivX <div class="Discussion_UserSignature"> </div>

 

[ramayana]

I thought 0 (zero) = undefined<br /><br />For instance a singularity with 0 volume, it's literally stating it's undefined or unknown? <br /><br />Isn't there a difference in our experienced definition of zero, versus the mathematical terminology?

 

[vandivx]

infinitesimal and infinite are the ones that are undefined since they do not have any particular value, that is they are not numbers or fractions of numbers<br /><br />on the other hand zero is defined very precisely, same as any number, it specifies no quantity or no amount, simply nothing<br /><br />singularity is a mathematical term which denotes a place or a point on a function where it is unbounded (discontinuous) and therefore undefined<br /><br /><blockquote><font class="small">In reply to:</font><hr /><p> http://en.wikipedia.org/wiki/Gravitational_singularity The simplest Big Bang cosmological model of the universe contains a causal singularity at the start of time (t=0), where all timelike geodesics have no extensions into the past. Extrapolating backward to this hypothetical time 0 results in a universe of size 0 in all spatial dimensions, infinite density, infinite temperature, and infinite space-time curvature.<p><hr /></p></p></blockquote><br /><br />zero volume implies those infinite undefined 'quantities' but I don't see how or why that would reflect back on the zero itself<br /><br />I don't believe that singularities actually exist in the real world, nature has mechanisms that prevent their formation via some runaway process and you could say it can't help preventing them because they are physical imposibilities<br /><br />if the gravitational or any other theory results in singularity then (in Einsteinian speak) it is incomplete theory which when completed it is implied will not have it (the singularity)<br /><br />vanDivX <div class="Discussion_UserSignature"> </div>

 

[ramayana]

Ahh, it's the division by zero that is undefined... My bad...