represent the set

JeffM said:
There you go. I edited the post you quoted.
Click to expand...
Now taking a fresher look at it after your explanation is plain to see that, definitely, 0 is the only number that satisfies the constraints set in the excercise.
 
I have kind of an afterthought type of question.
I know that brackets with nothing on it means an empty set
Bur what happens if within a set I have a number let's say in this example
A={0,3,−3,2,1,{2}}
How should I consider that 3?.
What is the difference between the 2 without the brackets and the two in the brackets?.
 
In a different response, I said that a number is an attribute of a set. If you are tall, “tall” is an attribute rather than a person, which is what you are.

The members of the set you are talking about are of two different things: numbers and sets of numbers.

It is sort of weird, and leads off into the theory of types, which I greatly doubt I can explain. The theory of types is supposed to prevent set theory from leading to paradoxes such as whether the set of every set that does not contain itself contains itself. PKA may be able to explain all this, but frankly, I do not consider this sort of question to be helpful to students.
 
JeffM said:
In a different response, I said that a number is an attribute of a set. If you are tall, “tall” is an attribute rather than a person, which is what you are.

The members of the set you are talking about are of two different things: numbers and sets of numbers.

It is sort of weird, and leads off into the theory of types, which I greatly doubt I can explain. The theory of types is supposed to prevent set theory from leading to paradoxes such as whether the set of every set that does not contain itself contains itself. PKA may be able to explain all this, but frankly, I do not consider this sort of question to be helpful to students.
Click to expand...
Okay, that is fair enough for me. Thank you for explaining all that.
 
Which of these are the empty set? Which of these sets contain the (symbol for the ) empty set?
{ φ }
φ
{ }
{ { } }
 
Jomo said:
Which of these are the empty set? Which of these sets contain the (symbol for the ) empty set?
{ φ }
φ
{ }
{ { } }
Click to expand...
According to what I am studying #3 represtns an empty set
And # 4 represents an empty set in an empty set.
 
This subject is kind of wierd
I have read that the empty set is not an element of every set. It may be an element of some sets. for example the set has the empty set as one of its elements but does not contain the empty set as one of its elements.
Hard to understand for me.
 
eddy2017 said:
According to what I am studying #3 represents an empty set
And # 4 represents an empty set in an empty set.
Click to expand...
Jomo said:
Which of these are the empty set? Which of these sets contain the (symbol for the ) empty set?
{ φ }
φ
{ }
{ { } }
Click to expand...
What about #1 and #2? Just recall that an alternate way of writing { } is φ
 
Didn't know that. That being the case they all represent empty sets then.
 
I asked a question before at post #23 . Do you know the answer to that?. JeffM gave an explanation but did not address the question as such.
 
I started studying about sets just last week and doing some exercises trying to get familiar with the skill. It is one the skills that is going to be tested at the exam.
I started with Khan academy in Spanish.
 
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This was my question back at post #23. There has to be an answer for that.
what happens if within a set I have a number let's say, in this example,
A={0,3,−3,2,1,{2}}
How should I consider the number 2?.
What is the difference between the 2 without the brackets and the two in the brackets?.
 
1) { φ }
2) φ
3) { }
4){ { } }

#2 and #3 are the empty set.
#1) Represents the set that has φ (a symbol for the empty) as its only element.
#4) Represents the set that has { } (a symbol for the empty) as its only element.

Questions for others. Since φ = { }, does {φ} ={ { } }?
I think it depends on how you interpret what is inside the set. In the 1st set, it has a circle with a line through it. In the 2nd set it has two strange looking brackets. Alternatively, both sets only have the symbol for the empty set in it.
 
Totally understood, prof!
If there is something inside the brackets that is considered an element even if it is the empty symbol. Then the empty symbol is considered an element. Got it.
 
Jomo said:
1) { φ }
2) φ
3) { }
4){ { } }

#2 and #3 are the empty set.
#1) Represents the set that has φ (a symbol for the empty) as its only element.
#4) Represents the set that has { } (a symbol for the empty) as its only element.

Questions for others. Since φ = { }, does {φ} ={ { } }?
I think it depends on how you interpret what is inside the set. In the 1st set, it has a circle with a line through it. In the 2nd set it has two strange looking brackets. Alternatively, both sets only have the symbol for the empty set in it.
Click to expand...
Just for clarity, the proper symbol for the empty set is not [imath]\varphi[/imath] or [imath]\phi[/imath] (the Greek phi), but the Scandinavian [imath]\varnothing[/imath].
 
I have seen that symbol in a video. But thanks for the clarification.
 
eddy2017 said:
I have seen that symbol in a video. But thanks for the clarification.
Click to expand...
Where have you seen any of [imath]\varphi ,{\kern 1pt} \;\phi ,\;\Phi [/imath] used as the symbol for the emptyset?
The standard notation is [imath]\emptyset[/imath] or maybe [imath]\cancel{O}[/imath].
It would serve you well to learn LaTeX coding.
 
pka said:
Where have you seen any of [imath]\varphi ,{\kern 1pt} \;\phi ,\;\Phi [/imath] used as the symbol for the emptyset?
The standard notation is [imath]\emptyset[/imath] or maybe [imath]\cancel{O}[/imath].
It would serve you well to learn LaTeX coding.
Click to expand...
What are you talking about?. I said, in response to what what Dr Peterson posted, that I have seen the scandinavian symbol being explained as the standard symbol for an empty set. That was what I was referring to. Take it down a notch will you? I'm being polite. No need to get upset. Take it easy. You are a teacher. Are you not?

I'm here to learn and if I don't know something I will ask. Iwill ask as many questions as I see fit to lead me to an understanding . It is your prerogative to help or not. But come correct or don't come at all!.

In the other thread you have already insulted me telling me that if I do not know something then I am wasting your time . You can remedy that really easily.
 
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