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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


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    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


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


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    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


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    Staff: Mentor

    Please check your PMs. The PF Rules require that you show some effort before we offer tutorial help.
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