   Ramanujan, Whom the Muses Loved
  Can anyone give me an intuition or explanation for why the following should hold?
Looks complicated :)   ;  Eh, that's trivially obvious. Really, if you can't figure out this for yourself, you have no business at this level.I win again, Lews Therin.;  Isnt it an incredible beauty and mystery of Nature that there are some numbers, that are indeed REAL (think of the diagonale of a 1m square, which length is sqrt(2)) that we will be unable to know for ever.I mean, draw a 1m square. It's diagonal is right here before your eyes, you can see it, you can touch it, but wtf, you can not measure it ! That reallyblows my mind every time I think about it. It's a damn great world we live in isnt it :)I apologize for that mostly (if not completely) un-useful post :)   ;  Yeah, that's true, but so is everything else in life. Anything you want to measure has to be measured up to a certain accuracy. Even if something has a measureable quantity that you can *calculate*, that doesn't mean you can measure it precisely. In fact, you never can.   ;  Just get a computer that can measure it to the Planck scale [wink]Nothing is smaller than that, so...   ;Quote:Original post by ProzakJust get a computer that can measure it to the Planck scale [wink]Nothing is smaller than that, so...Thats an interesting point ! Isnt there some kind of contradictory facts there ?On the one hand, our mathematics have demonstrated that some number cannon be evaluated with 100% exactitude, not even being writen in the form of "x/y" where x and y would be integer numbers (like 2/3 has no decimal value, but still can be writen as 2/3, unlike Pi or sqrt(2) for example)On the other hand, if one draws an 1.0000000000000000000 {...} 0000 meter square with perfect exactitude, it diagonale length has to be perfectly equal to something. But Physics theory tells us that that 'something' cant be measured with infinite precision (related to that Plank const). What does that mean ? Does it mean that such precision doesnt exist, and that (positive infinitesimal) number smaller that a certain value (related to plank const, again) are unbound to phisical reality ? (being just figures out of our imagination) Or that such precision is real but unmeasurable ? I mean, is are there smaller length than plank distance, but we just cant measure them because, well, because we cant, or cant we measure them because there just aren't...Damn, my brain's boiling right now :) I love that kind of methaphysical useless reflection !   