Between two units

Discussion in 'Physics & Math' started by qfrontier, Sep 27, 2003.

  1. qfrontier Captain Of Starship Registered Senior Member

    Messages:
    114
    Is it not true that between 1 and 2 there are an infinite number of smaller numbers? So, between two finite numbers, there is an infinity of numbers. IE: between 1 and 2 there is 1.1 and between 1 and 1.1 there is 1.01 and between 1.1 and 1.01 there is 1.001 and so on....So when we go from 1 to 2 we sort of take a leap through infinity and arrive at 1.5 and then from 1.5 to 2 we take another leap through infinity. Thus since infinite numbers make finite numbers which in turn make infinite numbers, then it must be that infinity can be finite because of all the finite numbers which make up infinity. How can this be explained?

    Please Register or Log in to view the hidden image!

     
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. John Connellan Valued Senior Member

    Messages:
    3,636
    1 and 2 are not finite numbers. They are (just numbers) on an infinite number line. The distance from 1 to 2 is indeed finite but it can be divided by an infinite number of infinitly small sub-units.
    This is the key. Anything which is not infinite can still be didvided infinitely.
     
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. qfrontier Captain Of Starship Registered Senior Member

    Messages:
    114
    How is it that between 1 and 2 there is finity?
     
  6. Google AdSense Guest Advertisement



    to hide all adverts.
  7. Dapthar Gone for Good. Registered Senior Member

    Messages:
    203
    The distance from 1 to 2 is not finite either, it is 2-1 = 1 = .9999999.... = &Sigma;<sub>n=1</sub><sup>&infin;</sup>(9&middot;(1/10)<sup>n</sup>)=9/(1-1/10)=1

    When one considers the real number system, it is the "least well defined system" until one takes a real analysis class, or learns of its construction somewhere else. For example, the integers are the "counting numbers" (both positive, negative, and 0), the rationals are the quotients of two integers, but the definition of the real number system is more complex. Technically, all real numbers can be defined as a Dedekind cut of the rational numbers. A Dedekind cut is essentially the set of all rational numbers that are less than the real number one seeks, thus the real number is defined to be the least upper bound (also called the supremum) of the cut.

    Example: 2<sup>1/3</sup>

    The cut for 2<sup>1/3</sup> is the set of all rational numbers in the open set {x rational:x<sup>3</sup> < 2}. The least upper bound of it is 2<sup>1/3</sup>.
     
  8. god-of-course Bluegoblin. Registered Senior Member

    Messages:
    234
    qfrontier:
    no.
     
  9. John Connellan Valued Senior Member

    Messages:
    3,636
    This is a very confusing thread but I would like to say what I think. The reason you have come to the above conclusion is becasue you were using infinitely small sub-units to divide the distance 1. If u use a distance of 1, 0.5 or indeed any other unit of distance (other than the infinitely small one) the distance is finite.

    Infinity is strange, I think it was James R who basically said that a distance of one can contain the same number of infinitely small parts as the distance of 100 or even infinity for that matter. Thats why I hate infinity and believe it cannot exist in the physical world.
     

Share This Page