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Math Help - the difference between implication and a logical implication

  1. #1
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    the difference between implication and a logical implication

    When does p implies q noted as p---->q,


    and when does p logically implies q noted as p====>q

    solid examples would help.

    in a mathematical proof we use logical implication or just simple implications
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  2. #2
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    Quote Originally Posted by triclino View Post
    When does p implies q noted as p---->q,
    and when does p logically implies q noted as p====>q
    In my view there is absolutely no difference is the two expressions.
    Now, be warned that I am also sure the there is out there somewhere an author and textbook that will take great exception with my thinking that. For example, I recall reviewing a logic textbook in the 70ís in which the author took some five pages to argue that there are no such things as propositions. He maintained there are only sentences that are true or false. I think I recall his going so far as to say those who talk about propositions are just idealists and Platonists.
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    Quote Originally Posted by Plato View Post
    I think I recall his going so far as to say those who talk about propositions are just idealists and Platonists.
    What do you mean idealists and Platonist
    Last edited by triclino; August 18th 2008 at 06:02 PM.
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  4. #4
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    Quote Originally Posted by triclino View Post
    What do you idealists and Platonist
    I cannot understand that statement.
    It appears that you have little understanding of the philosophy of mathematics, but that is the nature of your question. Do you know what you are asking about?
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    ok i was just browsing through some notes and came across the following. hope it helps ....

    The truth of p \rightarrow q is sometimes described by the expression "p is a sufficient condition for q" or "q is a necessary condition for p"

    example:

    p = "it is raining"
    q = "there are clouds in the sky"

    p \rightarrow q is true
    but q \rightarrow p is false.



    Given two compound propositions P and Q, we say that P logically implies Q, if Q has the truth value true whenever P has truth value true. we write P \Rightarrow Q when this occurs.
    Note that P \Rightarrow Q iff ( p \rightarrow q ) is a tautology.
    That is, P \Rightarrow Q \longleftrightarrow  (p \rightarrow q)
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  6. #6
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    Quote Originally Posted by Plato View Post
    I cannot understand that statement.
    It appears that you have little understanding of the philosophy of mathematics, but that is the nature of your question. Do you know what you are asking about?
    It appears that you have little understanding of logic.

    is part of the philosophy of mathematics ,for everyone to say
    what ever he likes about logic.
    Do you know how logic is used in a mathematical proof??
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