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Math Help - logic and proof

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    logic and proof

    What is wrong with this argument? Let S(x,y) b " x is shorter than y". Given the premise \left( {\exists x} \right) S(s,Max), it follows that S(Max,Max). Then by existential generalization it follows that \left( {\exists x} \right)S(x,x), so that someone is shorter than himself.
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    Quote Originally Posted by TheRekz View Post
    What is wrong with this argument? Let S(x,y) b " x is shorter than y". Given the premise \left( {\exists x} \right) S(s,Max), it follows that S(Max,Max). Then by existential generalization it follows that \left( {\exists x} \right)S(x,x), so that someone is shorter than himself.
    It only follows that S(x, Max) if there is such a y such that x < y for all s. This value of y need not exist.

    As an example, let the universe of discourse be the set  \{ 1 - n^{-1}| n \in \mathbb{Z}^+ \}. No Max exists such that S(x, Max) for all x.

    -Dan
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    I don't really get your explanation, could you try to explain it a bit more or maybe more examples. Sorry!

    I don't get the example that you give me, but I understand that in order of S(x,y) to be valid, x has to be less than y and here x = y, so it can't happen right? Am I explaining it the right way? I also don't understand by the domain that you give me. Is that for all x and y?

    Is this a type of fallacy?
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    Quote Originally Posted by TheRekz View Post
    What is wrong with this argument? Let S(x,y) b " x is shorter than y". Given the premise \left( {\exists x} \right) S(s,Max), it follows that S(Max,Max). Then by existential generalization it follows that \left( {\exists x} \right)S(x,x), so that someone is shorter than himself.
    Please sort out your notation

    RonL
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    Quote Originally Posted by TheRekz View Post
    Is this a type of fallacy?
    Yes the fallacy occurred in your first use of existential instantiation.
    The basic rule for EI is: \frac{{\left( {\exists x} \right)\phi (x)}}{{\phi (v)}} where v is an individual constant having no prior occurrence in the context.
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    so what type of fallacy is this? it it the affirming the conclusion?
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    Quote Originally Posted by TheRekz View Post
    so what type of fallacy is this? it it the affirming the conclusion?
    I have no idea what name your instructor/textbook would give to that fallacy. It is just a violation of the instantiation rules.
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