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