Observation 4

Ep. 267 Infinities

   The concept of infinity and zero are both relatively new concepts.  Infinity began to be discussed around 400 BC.  Zeno developed the concept of potential infinities and finite infinities.  Enumerable things are able to be counted and innumerable things are uncountable but are still limited.  Some examples would be the number of grains of sand on the beach.  Other things are not finite such as the expansiveness of a mathematical plane.  Another concept then developed of different quantities making up infinities.  The set of numbers is infinite as is the set of even numbers but the set of even numbers is less than the set of integers.  Countable infinities include all sets of integers.  Uncountable infinities include the list of all real numbers, including the numbers between each integer.  

    The infinity sign has debatable origins but most likely it was developed in 1655 by John Willis, a mathematician.  Some say it is based on Omega from the Greek alphabet which is the last letter.  The infinitesimal accompanies the concept of infinity and, like infinities, has different types.  

    The hotel or Hilbert's paradox states that a hotel with a finite number of guests, an infinity of new guests come in.  A countable infinity comes in as you add rooms and guests.  

    Applied to astronomy, an issue comes up when thinking about infinities and space.  If the universe in infinite in size and age, then whatever direction we look we should see a star.  This obviously does not occur in nature implying that the universe is either finite in age, size, or both.  The universe is most likely 13.7 billion years.  A multiverse is a theory that there are many universes similar to ours.