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!

A Logic Problem

  1. Feb 23, 2009 #1
    1. The problem statement, all variables and given/known data
    There exists y > 0 such that [[tex]y^{2} = x[/tex] if and only if [tex]x > 0[/tex]].

    This means that "there is some positive number whose square equals all positive
    numbers." - St. John College, Oxford

    3. The attempt at a solution
    I am not sure about this statement "- - some positive number whose square equals
    all positive numbers", and particularly about the word "all".

    I would read the statement as
    If [tex] \exists y > 0[/tex], then [tex]\exists [ y^{2} = x[/tex] if and only if [tex]x > 0] [/tex]

    It seems that the statement should be read as
    If [tex] \exists y > 0[/tex], then [tex]\forall [ y^{2} = x[/tex] if and only if [tex]x > 0] [/tex]

    Is there always "for all" after "such that"?
     
  2. jcsd
  3. Feb 23, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You don't say "there exists" a statement. "There exists" and "for all" only apply to variables.

    Not necessarily. There exist x> 0 such that x2= 4. That has no "for all". Try thinking about what "for all" means rather than looking for general rules.
     
  4. Feb 23, 2009 #3
    It seems that we need to make statements true for a given context.

    For example, the above example with "for all" is false, whereas right with the "exists". It is nonsense to say that there exists one positive real number whose square equals all positive numbers.

    The quantifiers apply to the variables. I agree with you about that.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: A Logic Problem
  1. Math logic problem (Replies: 2)

  2. Annoying Logic Problems! (Replies: 28)

Loading...