Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Measure of the reals

  1. Feb 13, 2013 #1
    I was reading a little about measure theory, and the measure of a singleton is zero.
    So why couldn't we just describe the reals as an uncountable number of singletons which each have zero measure and then union all of these singletons.
    Maybe the union only works for countable sets when talking about measure.
     
  2. jcsd
  3. Feb 13, 2013 #2

    jbriggs444

    User Avatar
    Science Advisor

    You are trying to apply the principle that the measure of a disjoint union is the sum of the measures of the components, right?

    How do you define the sum of an uncountable set of numbers?
     
  4. Feb 13, 2013 #3

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Literally looking 5 seconds at the wikipedia page on measure theory answers your questions: http://en.wikipedia.org/wiki/Measure_theory

    Please do some research yourself before asking questions.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Measure of the reals
  1. Real Numbers (Replies: 3)

  2. Real numbers ? (Replies: 4)

  3. On Real Enumeration (Replies: 20)

  4. Consecutive Reals (Replies: 39)

Loading...