1. Not finding help here? Sign up for a free 30min 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!

Proof by contradiction

  1. Sep 29, 2013 #1
    Prove by contradiction that a real number that is less than every positive real number cannot be positive

    having troubles with this

    could someone give me a small hint to get started?
     
  2. jcsd
  3. Sep 29, 2013 #2

    pasmith

    User Avatar
    Homework Helper

    Suppose [itex]x > 0[/itex] is such that every positive real number is greater than or equal to [itex]x[/itex]. What then is [itex]x/2[/itex]?
     
  4. Sep 29, 2013 #3
    I'm sorry but I can't seem to proceed even with this hint :(
     
  5. Sep 29, 2013 #4

    pasmith

    User Avatar
    Homework Helper

    Given that [itex]x[/itex] is a positive real number, is [itex]x/2[/itex] a positive real number?
     
  6. Sep 29, 2013 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I wouldn't even bother with x/2. Suppose x is positive. Can it then be "less than every positive number"
     
  7. Sep 29, 2013 #6

    berkeman

    User Avatar

    Staff: Mentor

    Please check your PMs. The PF Rules require that you show some effort before we offer tutorial help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Proof by contradiction
  1. Proof by contradiction (Replies: 1)

  2. Proof by contradiction (Replies: 2)

  3. Proof by contradiction (Replies: 6)

  4. Proof by contradiction (Replies: 4)

Loading...