Thread: Can a set have an absolute value?

I'm looking at a question which is asking me {x : x is a subset of {1, 2, 3, 4, 5} and |x| < 1}, list the elements of x.

I'm familiar with cardinality of sets, but i haven't seen, and can't find, anything that talks about an absolute value of a set.

does anyone know how to find them if they do exist?

Originally Posted by Relmiw

I'm looking at a question which is asking me {x : x is a subset of {1, 2, 3, 4, 5} and |x| < 1}, list the elements of x.

I'm familiar with cardinality of sets, but i haven't seen, and can't find, anything that talks about an absolute value of a set.

does anyone know how to find them if they do exist?

for a set A, |A| denotes the cardinality of the set A.

please check the problem to make sure you typed it out correctly, exactly as it was written. because as it stands now, this is a pointless exercise and the answer is the empty set. that's the only element that would be in this set. which it bothers me that you didn't give it a name...

The question is exactly:

"Find the cardinality of the following sets.

a. {x ⊆ {1, 2, 3, 4, 5} and |x| < 1}."

Originally Posted by Relmiw

The question is exactly:

"Find the cardinality of the following sets.

a. {x ⊆ {1, 2, 3, 4, 5} and |x| < 1}."

well, that's completely different from what you asked at first, Relmiw!

ok, so, what are the subsets of {1,2,3,4,5} that contain exactly one element (or less) in them?

ahh, ok. i get it now, thank you.

the cardinality is six
the subset is {{ }, {1}, {2}, {3}, {4}, {5}}

Originally Posted by Relmiw

ahh, ok. i get it now, thank you.

the cardinality is six
the subset is {{ }, {1}, {2}, {3}, {4}, {5}}

yes! brilliant!