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Help with an implications question?

Hi,

I've been given a worksheet aiming to help me use symbols like implies, for all, and there exists, better. I was asked to use these symbols to argue the truth or falsity of some statements. Now, I DO NOT want the answer given to me. I would just like clarification on the following two statements:

For each p there exists q such that q > p

For each p there exists q such that p < q

Is this a typo in the question or are these two statements one and the same? As I said, don't give me the answer (I think I've got it already anyways), but is there some subtle difference between the two? Thanks
Original post by Ktulu666
Hi,

I've been given a worksheet aiming to help me use symbols like implies, for all, and there exists, better. I was asked to use these symbols to argue the truth or falsity of some statements. Now, I DO NOT want the answer given to me. I would just like clarification on the following two statements:

For each p there exists q such that q > p

For each p there exists q such that p < q

Is this a typo in the question or are these two statements one and the same? As I said, don't give me the answer (I think I've got it already anyways), but is there some subtle difference between the two? Thanks


Assuming those signs (>,<) mean greater than and less than then I see no difference between the two mathematically.
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Ktulu666
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Original post by ghostwalker
Assuming those signs (>,<) mean greater than and less than then I see no difference between the two mathematically.


Thanks, I didn't think there was either, but I'm being enforced upon the importance of the little details when demonstrating statements etc, was just nice to get a second opinion.

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