How to list Elements In A Set
Listing elements in a set
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okay this problems one of my favorites
it's actually in my personal area of
interest called set theory this is the
beginning levels of what I'm very
interested in is a research topic so
we're gonna write the set as a list of
elements as opposed to what we call here
set builder notation where we just
describe a rule so I did Josh else in
here j j is equal to now this is read as
the set of Z's such that this vertical
line is such that Z is an integer needs
no decimal no fraction and negative 1 is
less than or equal to Z is less than 3
so first we put the beginning set theory
bracket or the Jay Leno brock and I like
the cool cuz it's got the big chin right
there so see C has to be an integer or
no decimal or fraction part and Z needs
to be in between negative 1 and 3
including negative 1 but not quite
including 3 so the number negative 1 was
acceptable because negative 1 is less
than or equal to negative 1 so is the
number 0 because that's in between
negative 1 and 3 so is the number 1 so
is the number 2 and notice that the
number 3 is not accepted here because 3
is less than 3 is not less than 3 2 is
less than 3 but 3 is not less Lutheran
so the final answer here would be the
set containing negative 1 0 1 2
okay pause the video and see if you can
do the second example on your own and
assuming you've taken a shot at it let's
do it together H is equal to the set of
T such that T is an integer and negative
three is less than T is less than two
this time this will be equal to the set
we need the integers that don't have any
decimal a fraction part and are located
strictly between negative 3 and 2 so
this time the left endpoint of negative
3 is not acceptable because we don't
have equal to here only less than
negative 3 has to be less than T so
we'll start at the number negative 2 and
start counting up negative 1 0 notice
will include 1 also because once in that
interval and yet again we do not include
the right endpoint 2 is not acceptable
here because 2 is not less than 2 2 is
equal to 2 so this is where we have to
end and so this set would be negative 2
negative 1 0 1
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