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Math 360 Assignment, math grammatically

  1. Aug 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Decide if each of the following is a sentence or not. If the item is a sentence, is it true or false? Give a reason for your answer. If it is not a sentence, identify the part of speech.

    x^2 - x - 12

    x^2 - x - 12 = 0

    x^2 - x - 12 = (x-3)(x+4)


    2. Relevant equations



    3. The attempt at a solution

    1.) I would call this a noun. "Equals n" or "is greater than n" are examples of verbs, which would make this a statement with verifiable truth or falsehood. Since it is not a sentence, no truth or falsehood exists.

    *2.) A question, but no statement. "Values of x where this is true." Although values exist, the statement taken as is doesn't have an inherent truth or falsehood.

    3.) A complete, true statement. "x^2 - x - 12" is the noun, and "equals (x+4)(x-3)" is a verb. The statement can be shown to be true with multiplication or factoring.

    (x+4)(x-3) = x^2 + 4x - 3x - 12 = x^2 - x - 12


    #2 is really the one I am unsure of. Do you all agree?
     
  2. jcsd
  3. Aug 23, 2011 #2

    berkeman

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    Staff: Mentor

    What in the world is Math 360?
     
  4. Aug 23, 2011 #3

    Mark44

    Staff: Mentor

    I would call #2 a sentence, but one that is true for some values of x, and false for others.

    Apparently what you are studying in your Math 360 class is categorizing things as nouns or sentences. The usual terminology would be that #1 is an expression, #2 is an equation that is true conditionally, #3 is an equation that is true unconditionally (an identity).

    I disagree with some of what you have. In #2 and #3, the verb is "=." To continue this grammar metaphor, what you're calling the verb should probably be called the predicate.

    As a non-mathematical example of something similar, "Fred is a salesman." The subject is "Fred," a noun. The verb is "is." The predicate is "is a salesman."
     
  5. Aug 23, 2011 #4
    Math 360 is "Foundations of Higher Mathematics" and required for Math majors with a pre-req of calc I. It's mainly proofs and logic, set theory and what not. Being the first day, I assume we start off basic.

    Thanks guys, I think this will be a pretty fun class.

    EDIT: Darn, #3 is false! I had a second glance.
     
    Last edited: Aug 23, 2011
  6. Aug 23, 2011 #5
    #3 is false [tex]{(x-3)(x+4)=x^{2}+4x-3x-12=x^{2}+x-12}[/tex]


    This sounds like a pretty interesting assignment!
     
  7. Aug 24, 2011 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    #2 is what is called an "open sentence". It is true for some values of x but not others.
     
  8. Aug 24, 2011 #7

    Mark44

    Staff: Mentor

    For #3, I didn't check the OP's factorization closely enough to notice that his signs were backward.
     
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