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Thread: quantities, values and symbols

  1. #1 quantities, values and symbols 
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    I've learned that the quantity time is represented by the symbol t.

    But is this statement correct, I've been thinking about this and seems to me that the symbol t represents the value of the quantity time, not the quantity itself.

    But sometimes in an other context it seems that the symbol t represents the quantity and not its value.

    Does it represent the quantity, the value or is it context dependent ?

    (I don't use the English language a lot, so please correct me if I don't use it well.)


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  3. #2 Re: quantities, values and symbols 
    . DrRocket's Avatar
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    Quote Originally Posted by kasper90
    I've learned that the quantity time is represented by the symbol t.

    But is this statement correct, I've been thinking about this and seems to me that the symbol t represents the value of the quantity time, not the quantity itself.

    But sometimes in an other context it seems that the symbol t represents the quantity and not its value.

    Does it represent the quantity, the value or is it context dependent ?

    (I don't use the English language a lot, so please correct me if I don't use it well.)
    You have a good point.

    The useage is often a bit ambiguous and it is left to the reader to make the proper interpretation.

    This is related to the notation for functions. In rigorous mathematical useage, a function f is denoted simply by the letter "f". f(x) is then the value of the function f at the point x. However, in elementary texts f(x) is often used to denote the function.

    Similarly, "t" is used to denote either the time function or a specfic value of time, the value of that function at some point.

    You will have to pay attention and recognize which is the proper interpretation based on the context. Physicists are sometimes rather sloppy about making the distinction, but it usually causes no confusion if the reader thinks about it for a bit, and it avoids an overly pedantic style of writing.


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  4. #3  
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    Okay, that's clear.

    New subject, variables.

    In physical context, the variable time stands for quantity with a variable value.
    and the constant c stand for a quantity with a constant value.
    The meaning of the symbols is context dependent.

    But how does it work in math?

    What does the variable x mean:
    1. the value, which may vary, of an unknown quantity x, or
    2. the value x, which may vary, of an unknown quantity
    3. or the just number x, which may vary

    I think it is option 3, because math doesn't refer to quantities, at least not in his physical meaning.

    There are no constant in math, or are there ?
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  5. #4  
    . DrRocket's Avatar
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    Quote Originally Posted by kasper90
    Okay, that's clear.

    New subject, variables.

    In physical context, the variable time stands for quantity with a variable value.
    and the constant c stand for a quantity with a constant value.
    The meaning of the symbols is context dependent.

    But how does it work in math?

    What does the variable x mean:
    1. the value, which may vary, of an unknown quantity x, or
    2. the value x, which may vary, of an unknown quantity
    3. or the just number x, which may vary

    I think it is option 3, because math doesn't refer to quantities, at least not in his physical meaning.

    There are no constant in math, or are there ?
    There are some constants in mathematics. For instance 1,2, 27, e, . A constant is just a number. We have quite a few numbers in mathematics.

    In math you need to understand the conventions being used by the author. I don't quite understand the difference among your 3 possibilities for x.

    In general x is used to represent some unknown number. But it is also used sometimes as the function that is projection on the first entry of an ordered pair, or ordered triple, etc. It is also use in more general contexts to represent some quantity belonging to some set that is specified by the author. Mathematics has few hard and fast conventions, and the degree of precision and rigor varies with the subject matter and the audience.

    One is sometimes a bit sloppy with undergraduates in an elementary class in order not to be too pedantic and thereby confuse naive students. One is sometimes sloppy with advanced graduate students and professionals because they know what is going on and one can skip some niceties and get to the point quickly without any fear of confrusing them. One is often overly precise in introductory classes for mathematics majors so that they can come to understand what rigor really is and learn to be precise and accurate. But a mathematician is never as sloppy as your average physicist, and never does someting (in public) that he cannot justify rigorously if needed.
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