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    How can you negate the following: ((x>y)⇒(x<z))

    How would you write that a polynomial has two distinct roots symbolically?
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    (Original post by lizzy21018)
    How can you negate the following: ((x>y)⇒(x<z))
    x&gt;y\not\Rightarrow x&lt;z or \neg (x&gt;y\Rightarrow x&lt;z) Edit: see below.

    (Original post by lizzy21018)
    How would you write that a polynomial has two distinct roots symbolically?
    \exists\,z_1,z_2\in\mathbb{C}:\;  \;p(z_1)=p(z_2)=0\wedge z_1 \neq z_2
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    (Original post by lizzy21018)
    How can you negate the following: ((x>y)⇒(x<z))
    I'd use (x&gt;y)\land \lnot(x&lt;z) or (x&gt;y)\land(x\geq z)

    (Original post by Lord of the Flies)
    x&gt;y\not\Rightarrow x&lt;z
    Is this a new standard? I've only seen it used twice (including this); both times on TSR in the last month. The other usage on here came from a book - can't recall the title, but I don't think it was specifically on logic.

    Seems a confusing symbol to me, since A does not imply B, in english, means A has no bearing on B, and not the logical usage given above.
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    (Original post by ghostwalker)
    Is this a new standard? I've only seen it used twice (including this); both times on TSR in the last month. The other usage on here came from a book - can't recall the title, but I don't think it was specifically on logic.

    Seems a confusing symbol to me, since A does not imply B, in english, means A has no bearing on B, and not the logical usage given above.
    I saw it in a book too, or rather a PDF I was reading on the internet. I thought about replying to the OP with the \geq example you gave, but then I figured the negation of "x>y necessarily implies x<z" would be "x>y does not necessarily imply x<z" rather than "x>y implies the opposite", in other words x >= z. But I see why this may be faulty logic.
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    (Original post by Lord of the Flies)
    ...
    Cheers. I think \not\Rightarrow is best avoided then.

    The standard negation of A\Rightarrow B is A\land \lnot B
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    (Original post by ghostwalker)
    Cheers. I think \not\Rightarrow is best avoided then.

    The standard negation of A\Rightarrow B is A\land \lnot B
    Thanks for letting me know, I'll bear that in mind!
 
 
 

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