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# Quantifiers and negation watch

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

How would you write that a polynomial has two distinct roots symbolically?
2. (Original post by lizzy21018)
How can you negate the following: ((x>y)⇒(x<z))
or Edit: see below.

(Original post by lizzy21018)
How would you write that a polynomial has two distinct roots symbolically?
3. (Original post by lizzy21018)
How can you negate the following: ((x>y)⇒(x<z))
I'd use or

(Original post by Lord of the Flies)
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.
4. (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 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.
5. (Original post by Lord of the Flies)
...
Cheers. I think is best avoided then.

The standard negation of is
6. (Original post by ghostwalker)
Cheers. I think is best avoided then.

The standard negation of is
Thanks for letting me know, I'll bear that in mind!

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