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what is the complement of R?

i do not know

i thought there are two types of numbers

the imaginary and the real

ok. thanks so much

so will that option b empty since is the complement of R?

So what is the answer?

Arbitrary in R

correct

i wonder how \(\{ x_n,\varnothing ,R
\}\) is considered cofinite :O

what does arbitrary really mean. because i see it as finite or infinite

um, it means if you close your eye and pick one

Arbitrary = any

he sucks with latex :)

he also usees \(\epsilon\) when he means \(\in\) so you got to be careful with that as well :)

oh i see now :)

but seriously start using \(\in\) when you mean in. It is coded as `\(\in)`

\in

\(\epsilon\), in general, means a positive real number

thank u sir

or "arbitrarily small" positive number :)

ok

What is that weird symbol?

empty set

then what is the 0?

its just zero

that makes no sense

or `\emptyset`

The union of any non empty set and anything else is non empty

these options don't make sense.

A⋂U=0

that is option a

A⋃U=\[ϕ \]

that is option b

A⋂U=\[ϕ \]

thats option C

A⋂U=X

option D

i think is option c

or option D

\(A\cap U \neq \emptyset\) is always true

i know option A and B are correct

but what about C and D?
i fink C is also correct

what does Y1isinR mean and why do you keep writing things like this?

that was how i saw it

\[Y_1 \] is in R

you look at the page and it looks like this ?
Y1isinR
?

i think that was what they wanted to write

what is \(Y_1\)?

do not have idea but is Every Hausdorff space is T1?

Tell me the definitions of both

X is a T1 space if any two distinct points in X are separated.

i know that Hausdorff space has to do with intersection. but what is really separated?

what does separated mean?

i asked the question

waw. so, T1 space is also Hausdorff space

we are not showing that T1 is Hausdorff, we are showing that Hausdorff is T1.

ok

i want to close the tab and open another. i think there are thinks i want to understand