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Thread: Discrete/Logic

  1. #1
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    Discrete/Logic

    Heres the problem



    Heres my attempt. I'm not sure if I have done it correctly, if not, am I on the right track?



    Edit: My answer is meant to be true, not false
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  2. #2
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    $\displaystyle \left[ {0 \in \mathbb{R}\backslash \mathbb{R}^ - } \right]\left[ {\forall y \in \mathbb{R}\backslash \mathbb{R}^ - } \right]\left( {0^2 < 1 + y} \right)$
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  3. #3
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    What are these R symbols?

    Was I totally wrong? Is what you wrote the solution?
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  4. #4
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    Quote Originally Posted by g4me View Post
    What are these R symbols?
    Was I totally wrong? Is what you wrote the solution?
    Although that is no absolute set of symbols in mathematics some notations are widely accepted. The symbol $\displaystyle \mathbb{R}$ is used to denote the real numbers. $\displaystyle \mathbb{R}^+$ denotes the positive reals and $\displaystyle \mathbb{R}^-$ denotes the negative reals.
    Thus $\displaystyle \mathbb{R}= \mathbb{R}^+ \cup \mathbb{R}^- \cup {0}$ so the nonnegative reals are $\displaystyle \mathbb{R}\backslash \mathbb{R}^ - = \mathbb{R}^ + \cup \{ 0\} $.

    As to the “Was I totally wrong?”, I really have no idea what you did. I cannot follow it. The symbolic statement reads “There is some nonnegative real number, x, having the property that for every real number y then $\displaystyle x^2<y+1$.
    You see that zero has that property; so does $\displaystyle \frac {1} {2}$.
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