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

This Question is Closed

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1Do you have a specific problem in mind? If so, please post it.

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0Not 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

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1Start with the properties attached in the file.

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1After you read them, go to the practice site at the following link: http://www.regentsprep.org/Regents/math/ALGEBRA/AN1/propPrac.htm

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0I know these properties already. The only property I don't understand is the closure property

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1Okay, 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)

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0Commutative Property because the values contained in the parenthesis stay the same, right?

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1Yes, very good. Most people focus on the three elements and answer "associative." Now for closure. See the two attached files.

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0Done. How would the problems look like?

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1Question 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?

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0But are there problems that look like For all real numbers a and b, {xx.....? My teacher seems to love those.

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1Your 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.

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0I'm not sure if I copied it down, but I'll check >.<

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0I can't find it, but the problems after the closure one all began with something likedw:1347588986815:dw

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1It'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?

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1So the two examples in the attached file are familiar? Yes?

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1What does the symbol on the attached file mean?

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1Right. So, the question I have is "What specifically is your question regarding set notation and closure.?" It seems that you know the lingo.

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0I 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.

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1If 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.

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0In which lies the problem... One more thing. Is: \[\sqrt{2}+3 is a real number\] an example of the Closure Property of Addition?

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0@Directrix . Last thing. I promise.

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1The 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?

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0I just know that ii=0, but I'm not sure if you can repeat the elements of the set

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1They 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?

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1Correct. Is the set of irrational numbers closed with respect to a) subtraction; b) multiplication?

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1Correct on both. Question: The sum of the conjugate complex numbers (a+bi) and (abi) is a real number. Does this violate the closure property for addition of complex numbers?

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0No? I mean, they're both real and imaginary but the result is 2a, so I'd imagine that it wouldn't violate it oo

Directrix
 2 years ago
Best ResponseYou've already chosen the best response.1The reals are a subset of the complex numbers so the closure property would not be violated. Your answer is correct.
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