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Math Help - What is a term?

  1. #1
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    What is a term?

    Work with them all the time, but I don't recall a formal definition of one (such a definition should take into account complex fractions I feel).
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    I would define a term along the lines of any numbers/variables which are not separated by a + or - sign it's by no means a real definition. Instead

    any distinct quantity contained in a polynomial; "the general term of an algebraic equation of the n-th degree": http://wordnetweb.princeton.edu/perl/webwn?s=term
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    I once tried to find a "precise" definition of term to put in a book I was writing, but a universal definition doesn't seem to exist (if it does, someone please tell me). But the idea is exactly what e^{ipi} said. expressions separated by + and - signs are terms.

    There are of course other definitions of terms used in different branches of mathematics, but I think this is the one you mean.

    In a complex fraction, for example, there will be terms in both the numerator and denominator of the complex fraction, and some of the terms will be fractions themselves.
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    Hello, wonderboy1953!

    Work with terms all the time, but I don't recall a formal definition of one.

    I was taught that a term is an expression consisting of multiplication only.

    . . So that: . 2x^3y^4,\;5\sqrt{a},\;x^3e^{2x}\ln(y) are all terms.


    I was also told that terms are separated by addition and/or subtraction.

    . . So that: /  2a + 3b has two terms (a binomial).
    . . . . . . . . . x^2 - 5x + 6 has three terms (a trinomial).

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  5. #5
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    it's quite common for students to confuse "terms" and "factors"
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    Quote Originally Posted by wonderboy1953 View Post
    Work with them all the time, but I don't recall a formal definition of one (such a definition should take into account complex fractions I feel).
    a term is something that is separated by a + sign. For 2x-2y+3. The terms are 2x, -2y, 3.
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    Quote Originally Posted by Barthayn View Post
    a term is something that is separated by a + sign. For 2x-2y+3. The terms are 2x, -2y, 3.
    (not picking on you) would you consider the following a term?: (x + y) as in (x + y) + 2 e.g..

    There are so many situations where it's gotten to the point that maybe the word term can't be defined in a consistent manner.
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    Quote Originally Posted by wonderboy1953 View Post
    (not picking on you) would you consider the following a term?: (x + y) as in (x + y) + 2 e.g..

    There are so many situations where it's gotten to the point that maybe the word term can't be defined in a consistent manner.
    I would consider that as two terms (x+y) with (x+y)+2 as three terms.

    Often we start off assuming it to be a single term to make it easier: (x+y-2)(x+y+2) = ((x+y)-2)((x+y)+2). In initially treating it as one term we see it's the difference of two squares: (x+y)^2-4. However, that (x+y)^2 will need to be expanded using the binomial theorem
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    Quote Originally Posted by e^(i*pi) View Post
    I would consider that a trinomial
    Going by what you're indicating, then there would be altogether seven terms in the expression.
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  10. #10
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    I believe that there necessarily has to be some ambiguity in the definition of a term. Here is a specific example showing why:

    I think that we would all agree that the expression 2(x + y) has only 1 term (however it has 2 factors, and one of those factors has 2 terms)
    So what about the expression 1(x + y)? As written it looks like it has only 1 term. But it is the same as x + y which clearly has 2 terms.

    Thus, it seems that there is no well-defined function f from expressions to positive integers which says how many terms are in the expression. That is, there is no function f such that if the expression E is equivalent to the expression E', then f(E)=f(E').


    Compare this situation to the model theoretic definition of term which is well-defined.
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