hey doctor peyam hello hi and today i will show you how to graph this thing which is
called the topologist sine curve notice there are really two parts in this definition first
is the segment from x equals zero and y ranging from minus one to one okay minus one to one
and the other part is really the cross oh that's just a vertical line now literally
oh no no no no no the first part when x is equal to zero and the absolute value of y is less than
or equal to one that's just that's just a fancy way to say it's a vertical segment oh in fact
notice what's cool is the set of limit points of that curve is precisely that segment sure okay
i don't understand for sure it means that no matter what output you have here you can kind
of take a specific roller coaster on this function and eventually end up at this point okay and you
feel very sick okay yeah and how do they kill the circle they just attached the circle to it
well they just identify no no no no isn't this the bottom part for this graph no what do you mean if
you look at the book yes my my favorite book okay yeah then i mean i i guess no you can just attach
yeah you can attach this segment to this here but there's none of that in the definition though
what about periodicity i mean you identify this open interval with periodic functions
no i i how did they get the bottom part from the definition huh but you just identified
okay i i it's point but it's not in there it's not in the definition i know but let's say functions
on the interval zero comma two pi okay with the same endpoints you can identify it as a circle
this is zero and this is two pi what are we talking about you are asking me why this no
no no no what math is this topology wow you know the doughnut equals coffee thing so you are saying
that this means a circle yes because you can take this dog i see three circles by the way oh one
two you can take this and just attach it to here so take this do whoosh and then voila circle
where this is you know zero and this equals to pi wow identify i'm going to
pretend that i understand otherwise i was someone also gonna pretend i understand it
that's the thing with teaching you don't have to understand everything you say
are you sure you just have to be confident
i do not do sometimes but hey the point is no i don't get how they end up with the bottom part
like you're not supposed to grab that bottom part if you don't have that in the equations
what are the definition let's see none of that says that you have the bottom part yeah but
think of it almost as a you know like this warping thing like you know you hear and then you teleport
yourself to here i understand that but it's still in the definition see this part this part
yeah it's the wrist segment i get that that part it's the calculus usual thing is that this thing
i get that but how are they able to just like connect that bottom circle show me the book again
yeah that part like that part what next this part this latinas is that they did not say that
it's implicit in the definition
fine now sometimes you can say things without saying that
i okay i'm going to just stop recording this is weird