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Grazes Group Title

Can someone explain to me what closure property is and how to identify it from an equations?

  • 2 years ago
  • 2 years ago

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  1. Directrix Group Title
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    Do you have a specific problem in mind? If so, please post it.

    • 2 years ago
  2. Grazes Group Title
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    Not really. I have a math teacher that assumed we learned this already and it's not in the math textbook. I just need help with the problems where you identify the property ex. 3+(4+5)=3+(5+4) Commutative property

    • 2 years ago
  3. Directrix Group Title
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    Start with the properties attached in the file.

    • 2 years ago
  4. Directrix Group Title
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    After you read them, go to the practice site at the following link: http://www.regentsprep.org/Regents/math/ALGEBRA/AN1/propPrac.htm

    • 2 years ago
  5. Grazes Group Title
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    I know these properties already. The only property I don't understand is the closure property

    • 2 years ago
  6. Directrix Group Title
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    Okay, I want to ask you to answer this question first. Thanks. Name the property: For real numbers, a, b, and c, give the property that justifies the following: a + (b + c) = a + (c + b)

    • 2 years ago
  7. Grazes Group Title
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    Commutative Property because the values contained in the parenthesis stay the same, right?

    • 2 years ago
  8. Directrix Group Title
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    Yes, very good. Most people focus on the three elements and answer "associative." Now for closure. See the two attached files.

    • 2 years ago
  9. Grazes Group Title
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    Done. How would the problems look like?

    • 2 years ago
  10. Directrix Group Title
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    Question 1: Is the set of negative integers closed under the operation of multiplication? Questions 2: Is the finite set { -1, 0, 1 } closed under the operation of division?

    • 2 years ago
  11. Grazes Group Title
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    Q1: No Q2: No

    • 2 years ago
  12. Grazes Group Title
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    But are there problems that look like For all real numbers a and b, {x|x.....? My teacher seems to love those.

    • 2 years ago
  13. Directrix Group Title
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    Your answers to Q1 and Q2 are correct. That is set notation your teacher is using. If you would look in your notes and find one of those problems and post it here, that would be good. We could discuss it.

    • 2 years ago
  14. Grazes Group Title
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    I'm not sure if I copied it down, but I'll check >.<

    • 2 years ago
  15. Grazes Group Title
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    I can't find it, but the problems after the closure one all began with something like|dw:1347588986815:dw|

    • 2 years ago
  16. Directrix Group Title
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    It's always good to take notes even if you understand what is being said at the time. I'll look in my books for a problem in that form. Question: Do you know the components of set builder notation?

    • 2 years ago
  17. Grazes Group Title
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    Yep.

    • 2 years ago
  18. Directrix Group Title
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    So the two examples in the attached file are familiar? Yes?

    • 2 years ago
  19. Directrix Group Title
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    What does the symbol on the attached file mean?

    • 2 years ago
  20. Grazes Group Title
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    Or does not

    • 2 years ago
  21. Directrix Group Title
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    Right. So, the question I have is "What specifically is your question regarding set notation and closure.?" It seems that you know the lingo.

    • 2 years ago
  22. Grazes Group Title
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    I have a test tomorrow and I'm just afraid that the closure problem will be something completely unexpected so I wanted to find someone who might know.

    • 2 years ago
  23. Directrix Group Title
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    If you had an example of just one problem which you have in mind as a "closure problem," then that would be a good place to start.

    • 2 years ago
  24. Grazes Group Title
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    In which lies the problem... One more thing. Is: \[\sqrt{2}+3 is a real number\] an example of the Closure Property of Addition?

    • 2 years ago
  25. Grazes Group Title
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    @Directrix . Last thing. I promise.

    • 2 years ago
  26. Directrix Group Title
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    The math processor is at 0% so I can't read the equation editor items with clarity. I think the question is the following: "(Is square root of 2) + 3 a real number. Yes, it is because square root of 2 is a real number and 3 is a real number and the set of real numbers is closed under the operation of addition. Look over your notes and ask other questions if you want. I don't mind. Question for you: Is the set of imaginary numbers closed under the operation of subtraction?

    • 2 years ago
  27. Grazes Group Title
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    I don't think so.

    • 2 years ago
  28. Grazes Group Title
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    I just know that i-i=0, but I'm not sure if you can repeat the elements of the set

    • 2 years ago
  29. Directrix Group Title
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    They are not. A counterexample to the statement that the set of imaginary numbers is closed with respect to subraction would be the following: 5i and 5i are imaginary numbers but 5i - 5i = 0i = 0 which is not an imaginary number. Question: Is the set of rational numbers closed with respect to multiplication?

    • 2 years ago
  30. Grazes Group Title
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    Yes.

    • 2 years ago
  31. Directrix Group Title
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    Correct. Is the set of irrational numbers closed with respect to a) subtraction; b) multiplication?

    • 2 years ago
  32. Grazes Group Title
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    a)no b)no

    • 2 years ago
  33. Directrix Group Title
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    Correct on both. Question: The sum of the conjugate complex numbers (a+bi) and (a-bi) is a real number. Does this violate the closure property for addition of complex numbers?

    • 2 years ago
  34. Grazes Group Title
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    No? I mean, they're both real and imaginary but the result is 2a, so I'd imagine that it wouldn't violate it o-o

    • 2 years ago
  35. Directrix Group Title
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    The reals are a subset of the complex numbers so the closure property would not be violated. Your answer is correct.

    • 2 years ago
  36. Grazes Group Title
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    Do I pass yet? :P

    • 2 years ago
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