represent the set

eddy2017

eddy2017

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Oct 27, 2017
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Hi, this is another exercise with sets.
1640462275623.png

represent the set where
y{ h|h is greater than 2 and less than 2}

after trying two times i tried 0 and it verified, but I need to know why.
the only plausible explanation is because >2 <2 then that invalidates it.
Is the reasoning good?
 
0 checked out. OK
That would mean that 0<2 and 0>2. Do you agree with this?

Also, there are numbers less that 2 other than 1, 0, -1, -2, ....
How about pi/2, 3/11, -e^4, 25/14
 
Jomo said:
0 checked out. OK
That would mean that 0<2 and 0>2. Do you agree with this?

Also, there are numbers less that 2 other than 1, 0, -1, -2, ....
How about pi/2, 3/11, -e^4, 25/14
Click to expand...
No, you're right. 0 can't be included because 2 is not greater than 0
 
So how would the solution be
h such as h is >2 and <2 ?

Choice
-2, -1, 0, 1, 2
Interesting. I'm in doubt now
 
So?.
No solution is possible. Can't think of nothing else
 
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Jomo said:
0 checked out. OK
That would mean that 0<2 and 0>2. Do you agree with this?

Also, there are numbers less that 2 other than 1, 0, -1, -2, ....
How about pi/2, 3/11, -e^4, 25/14
Click to expand...
I think you're right when it comes to 0 being > than 2
As to the other numbers that may be between 2 and -1 they are not expressed in the answer choice. I take it to mean the exercise doesn't want you to consider them.
Just the ones that have been listed to be in the set.
 
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eddy2017 said:
I think you're right when it comes to 0 being > than 2
As to the other numbers that may be between 2 and -1 they are not expressed in the answer choice. I take it to mean the exercise doesn't want you to consider themm
Just the ones that Jahe been listed to be in the set.
Click to expand...
Do you know the DEFINITION of "Null Set" ?
 
Subhotosh Khan said:
Do you know the DEFINITION of "Null Set" ?
Click to expand...
This is a null set
Any set that does not contain any element is called the empty or null or void set. The symbol used to represent an empty set is – {} or φ

Then, this is a null set, because it doesn't satisfy the demand of the exercise.
What I found strange is that there is no choice for that in the answer choice given. 0 is in the choice though.

Can a null set be 0?
 
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Null set means there is nothing in it.
If we compared it to zero then zero is a number therefore null set and 0 are different
Eg:
{0} is a set with one number inside
 
There is only one null set. This is a subtle point. In MOST cases, number is just ONE of multiple possible way to categorize sets.

For example, we might have a set of three dogs and a different set of three cats. Those sets agree in number, but not in type of member. Alternatively, we might have a set of three bottles of milk and a different set of four bottles of milk. Those sets agree in type of member but not in number. In other words, number is a way to categorize sets, but we can usually distinguish between different sets that have the same number.

However, there is no way to distinguish different characteristics of nothing. So the null set is necessarily unique.

But you are correct that the name of the number that characterizes the null set is zero.
 
JeffM said:
There is only one null set. This is a subtle point. In MOST cases, number is just ONE of multiple possible way to categorize sets.

For example, we might have a set of three dogs and a different set of three cats. Those sets agree in number, but not in type of member. Alternatively, we might have a set of three bottles of milk and a different set of four bottles of milk. Those sets agree in type of member but not in number. In other words, number is a way to categorize sets, but we can usually distinguish between different sets that have the same number.

However, there is no way to distinguish different characteristics of nothing. So the null set is necessarily unique.

But you are correct that the name of the number that characterizes the null set is zero.
Click to expand...
What do you think of the case at hand?. Is the exercise wrongly constructed or is there a solution?
 
Any real number is either greater than 2, equal to 2, or less than 2.

Do you agree?

Case 1. Any number > 2. Is that number also < 2.? No. So the number of numbers that are greater than 2 and also less than 2 is zero.

Case 2. The number is 2. Is 2 greater than 2? No. Is 2 less than 2? No. So the number of numbers that are 2 and both greater and less than 2 is zero.

Case 3. Any number < 2. Is that number also > 2? No. So the number of numbers that are less than 2 and also greater than 2 is zero.

0 + 0 + 0 = what?

I admit I do not like the way the problem is presented but I remember enough Spanish to know that “y” means “and”
 
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JeffM said:
Any real number is either greater than 2, equal to 2, or less than 2.

Do you agree?

Case 1. Any number > 2. Is that number also < 2.? No. So the number of numbers that are greater than 2 and also less than 2 is zero.

Case 2. The number is 2. Is 2 greater than 2? No. Is 2 less than 2? No. So the number of numbers that are 2 and both greater and less than 2 is zero.

Case 3. Any number < 2. Is that number also > 2? No. So the number of numbers that are less than 2 and also greater than 2 is zero.

0 + 0 + 0 = what?
Click to expand...
0
 
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