consider the following set of numbers

eddy2017

eddy2017

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Hi, I need your conformation of this solution.
consider the following set of numbers:

A={0,3,−3,2,1,{2}}

which of the following is true?
  • 4 ∈ A false
  • 2 ∉ A false
  • {3} ∈ A true
  • {2}∈ A true
    thanks,
    eddy












 
[math]{3}\in A[/math] is false, but [math]{3}\subset A[/math] is true...
 
eddy2017 said:
Hi, I need your conformation of this solution.
consider the following set of numbers:

A={0,3,−3,2,1,{2}}

which of the following is true?
  • 4 ∈ A false
  • 2 ∉ A false
  • {3} ∈ A true
  • {2}∈ A true
    thanks, eddy
Click to expand...
Two of those are correct and two are incorrect!
 
eddy2017 said:
how about a set with a single number, since it is enclosed in brackets. that is the only one explanation for those brackets around 2.
Click to expand...
I agree that '{2}' means a set with a single member 2.
 
pka said:
Two of those are correct and two are incorrect!
Click to expand...
well, 4 definitely does not belong in the set. that is one correct.
2 belongs and it says it does not. this is the other one correct
the other two.... uhmm
 
and {3} is the same case as {2} then. It is a set so does not belong.
 
to lev, blamocur, and pka , merry Christmas. My best wishes for 2021 and my deepest appreciation for your help
 
eddy2017 said:
Hi, I need your conformation of this solution.
consider the following set of numbers:

A={0,3,−3,2,1,{2}}

which of the following is true?
  • 4 ∈ A false
  • 2 ∉ A false
  • {3} ∈ A true
  • {2}∈ A true
Click to expand...
The notation {2} means that the set containing 2 is an element of the set -- so technically they are wrong in calling this a "set of numbers"! It is a set containing some numbers and a set.

You might think of a set as a bag containing things, and this bag contains a little bag that contains the number 2, along with some "free" numbers that are elements of the set directly.

So:
  • 4 is not an element of the set, so the first statement is false. (It is not mentioned at all.)
  • 2 is an element of the set, so the second statement is false. (2 is listed both as a free element and as an element of a set.)
  • {3} is not an element of the set, so the third statement is false. (3 is an element of the set, not of a set inside the set.)
  • {2} is an element of the set. so the fourth statement is true. (2 is both an element in its own right, and an element of a contained set.)
 
eddy2017 said:
well, then, after blamocur's confirmation then {2} does not belong either. Because it is a set in and of itself.
Click to expand...
Cannot agree with this one: a set can be a member of another set, not necessarily "in and of itself".
 
Dr.Peterson said:
The notation {2} means that the set containing 2 is an element of the set -- so technically they are wrong in calling this a "set of numbers"! It is a set containing some numbers and a set.

You might think of a set as a bag containing things, and this bag contains a little bag that contains the number 2, along with some "free" numbers that are elements of the set directly.

So:
  • 4 is not an element of the set, so the first statement is false. (It is not mentioned at all.)
  • 2 is an element of the set, so the second statement is false. (2 is listed both as a free element and as an element of a set.)
  • {3} is not an element of the set, so the third statement is false. (3 is an element of the set,
  • Dr.Peterson said:
    The notation {2} means that the set containing 2 is an element of the set -- so technically they are wrong in calling this a "set of numbers"! It is a set containing some numbers and a set.

    You might think of a set as a bag containing things, and this bag contains a little bag that contains the number 2, along with some "free" numbers that are elements of the set directly.

    So:
    • 4 is not an element of the set, so the first statement is false. (It is not mentioned at all.)
    • 2 is an element of the set, so the second statement is false. (2 is listed both as a free element and as an element of a set.)
    • {3} is not an element of the set, so the third statement is false. (3 is an element of the set, not of a set inside the set.)
    • {2} is an element of the set. so the fourth statement is true. (2 is both an element in its own right, and an element of a contained set.)
    Click to expand...

  • not of a set inside the set.)
  • {2} is an element of the set. so the fourth statement is true. (2 is both an element in its own right, and an element of a contained set.)
Click to expand...
{3} is not an element. good. I got that one wrong. confused on that. Now I see it. Got 3 out of 4!.
pka you were wrong when you say two correct two wrong!.
 
Dr.Peterson said:
The notation {2} means that the set containing 2 is an element of the set -- so technically they are wrong in calling this a "set of numbers"! It is a set containing some numbers and a set.

You might think of a set as a bag containing things, and this bag contains a little bag that contains the number 2, along with some "free" numbers that are elements of the set directly.

So:
  • 4 is not an element of the set, so the first statement is false. (It is not mentioned at all.)
  • 2 is an element of the set, so the second statement is false. (2 is listed both as a free element and as an element of a set.)
  • {3} is not an element of the set, so the third statement is false. (3 is an element of the set, not of a set inside the set.)
  • {2} is an element of the set. so the fourth statement is true. (2 is both an element in its own right, and an element of a contained set.)
Click to expand...
thank you for the explanation. very helpful!. Merry Christmas if celebrated.
 
The elements in a set are separated by commas. A set can have anything in it. After all, a set is just a collection of objects.

Some elements are 3, {1,2}, pi/3, *, &, # and 2/3.

In the set A = {1, {2,*}, @, y, 11/3}, the elementals are 1 and {2,*} and @ and y and 11/3. The set A does not contain 2. The set A does not contain *. The set A does not contain 13. The set A does contain 11/3. The set A does contain {2,*}.
 
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