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Math Help - [SOLVED] Question about logical signs

  1. #1
    MHF Contributor arbolis's Avatar
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    [SOLVED] Question about logical signs

    I have a question.
    I've never seen the logical sign "almost equivalent to". Does it exist? If not, why not? To say it's useless, for me it's like saying the sign " >" is useless since you always can write what you want using the " <" sign. (Of course if I'm right).
    I give you an example of when I find it useful : Say we write \frac{1}{100001} \frac{1}{100000}. Why wouldn't we write \frac{1}{100001} \frac{1}{100000} is "almost equivalent" to say \frac{1}{100002} \frac{1}{100000}?
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    Quote Originally Posted by arbolis View Post
    I have a question.
    I've never seen the logical sign "almost equivalent to".
    No it does not exist in mathematics.
    Because mathematics must be exact.
    Any person who is not exact in mathematics is a heretic!
    And must be burned at the stake.

    Just think about it. What does "almost approximately" even mean ?

    It is however used by phycisists. You know what that means!
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    MHF Contributor arbolis's Avatar
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    No it does not exist in mathematics.
    Because mathematics must be exact.
    Any person who is not exact in mathematics is a heretic!
    And must be burned at the stake.
    ahahah!!
    Just think about it. What does "almost approximately" even mean ?

    It is however used by phycisists. You know what that means!
    Yes I know what you mean. My brain formed this question while I was in a physics-lab class. Note that I wrote "almost equivalent" and not "almost approximately".
    I know you hate Numerical Analysis, but the "≈" is commonly used in this branch. Whatever, I'll be waiting for someone to propose the sign "almost equivalent" and it to be accepted.
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    \epsilon can be understood to be a very, very, very small number.

    0\;<\;x-\alpha\;<\;\epsilon

    This might read, "x is just barely not \alpha"

    Infinite Series provides another methodology.

    x\;=\;\alpha\;+O\left(h^{12}\right)

    This might read, "x is equivalent to \alpha if we ignore terms of some very high order, 12 in this case."
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    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by TKHunny View Post
    \epsilon can be understood to be a very, very, very small number.

    0\;<\;x-\alpha\;<\;\epsilon

    This might read, "x is just barely not \alpha"

    Infinite Series provides another methodology.

    x\;=\;\alpha\;+O\left(h^{12}\right)

    This might read, "x is equivalent to \alpha if we ignore terms of some very high order, 12 in this case."
    Yes, you are absolutely right. But I think you misunderstood me. I was talking about a sign that would looks like the \Leftrightarrow one, but from which it would differ as the ≈ differs from the = sign. I put an example with 2 numbers almost equal but what I wanted was to put emphasis on the relationship between the 2 sentences "" and " ".
    In other words, it's not right to say \frac{1}{100001} \frac{1}{100000} \Leftrightarrow \frac{1}{100002} \frac{1}{100000}, but what I'm saying is that it would be right to say it is "almost equivalent". Do you understand me?
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    No, I did not misunderstand, I was just trying to lean you away from your need to invent more notation. It's okay if some things don't have one, tiny, compact symbol in order to be expressed.

    Many years ago, I was trying variations of "=" to imply "must equal" and "better be equal" and a few other things. One assignment came back with large red ink and multiple circles around one of my new symbols. The red text read, "Please don't invent new notation. There is already far too much."

    Not everyone necessarily will agree, but he convinced me that day to stick to inventions that are necessary, not just convenient.
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    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by TKHunny View Post
    No, I did not misunderstand, I was just trying to lean you away from your need to invent more notation. It's okay if some things don't have one, tiny, compact symbol in order to be expressed.

    Many years ago, I was trying variations of "=" to imply "must equal" and "better be equal" and a few other things. One assignment came back with large red ink and multiple circles around one of my new symbols. The red text read, "Please don't invent new notation. There is already far too much."

    Not everyone necessarily will agree, but he convinced me that day to stick to inventions that are necessary, not just convenient.
    Ok, so I misunderstood you. I didn't want to invent anything (I'd let others to do so), I was just asking if such a symbol exist, and also if not, why not? But that's ok, it's nearly useless I agree, but so is >. For example if you want to say 5 is greater than 2, just type 2<5 which reads 2 is lesser than 5 which is equivalent to 5 is greater than 2.
    I was just wondering why symbols like > (and probably others) would be used and not one like "almost equivalent". Now I'm guessing it's because the symbol > would be far more used than the "almost equivalent to" one.
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    Well, we do have in rather common usage ">>" lots greater than and "<<" way less than. Why not a small verison.
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