1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inequality with infinity

  1. Nov 13, 2015 #1
    Is this true?
    ( - 1) <
     
  2. jcsd
  3. Nov 13, 2015 #2
    No. Infinity is not a number, so ordinary arithmetic doesnt apply.
     
  4. Nov 13, 2015 #3

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    For this you will need to define exactly what you mean with infinity. There are multiple notions of infinity, some notions where the above is true, some where it isn't true. But there is no standard notion of what ##\infty## means.
     
  5. Nov 13, 2015 #4

    fresh_42

    Staff: Mentor

    How? The smallest cardinal number is countably infinite and it doesn't matter whether you add 1 or not.
     
  6. Nov 13, 2015 #5

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    There are more notions of infinity than the cardinal or ordinal numbers.
     
  7. Nov 13, 2015 #6

    fresh_42

    Staff: Mentor

    What do you mean?
     
  8. Nov 13, 2015 #7

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    The class of cardinals numbers is one where ##\aleph_0 - 1## doesn't even exist.
    There is a number system (e.g. the affine real line ##\mathbb{R}\cup \{-\infty,+\infty\}##), where ##\infty - 1## exists an is equal to ##\infty##.
    There is a number system (e.g. the surreals) where ##\infty-1## exists and is distinct from ##\infty##.
     
  9. Nov 13, 2015 #8

    fresh_42

    Staff: Mentor

    Thank you. (definitely not meant ironic; those somehow esoteric concepts didn't come to my mind)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Inequality with infinity
  1. Infinity ? (Replies: 3)

  2. Is infinity = infinity? (Replies: 20)

  3. An inequality (Replies: 11)

Loading...