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Math Help - Determine whether these are valid arguments

  1. #1
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    Determine whether these are valid arguments

    1) If x is a positive real number, then x^2 is a positive real number. Therefore, if a^2 is positive, where a is a real number, then a is a positive real number.
    2) If x^2 /= 0, where x is a real number, then x /= 0. Let a be areal number with a^2 /= 0; then a /= 0
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  2. #2
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    Quote Originally Posted by ilovemymath View Post
    1) If x is a positive real number, then x^2 is a positive real number. Therefore, if a^2 is positive, where a is a real number, then a is a positive real number.
    This is not valid. \displaystyle a^2 \implies a = \pm\sqrt{a^2}
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  3. #3
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    Quote Originally Posted by ilovemymath View Post
    2) If x^2 /= 0, where x is a real number, then x /= 0. Let a be areal number with a^2 /= 0; then a /= 0
    The words "if", "then", "where", etc. don't cease to have their usual meanings because they are used in a mathematical context. Consider this argument: "If x has gills, where x is a vertebrate, then x lives in water. Let Blinky be a vertebrate with gills; then Blinky lives in water."
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  4. #4
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    This is not valid since a^2 is positive whether a is positive or negative...
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