Brian L

I just bought myself a bottle of Cantillon Kriek, a fruit lambic. Right now it's at cellar temp, anyone know if I should chill it a bit before I drink it?

Cheers.

I just finished a bottle of Paulaner Salvator... next up is Chimay. mmmmm

best answer goes to the person drinking the best beer.

cheers.

Why do you believe in your deity(ies) and not another one?

When did you decide? And how did you decide?

*Note: saying that your specific religious text revealed the truth is not a good argument. Why do you hold your specific religious text(s) above others?

Ok, bear with me here because this is an honest question. I'm basing this question on the following things which I'm supposing to be true.

1. God has some type of physical manifestation (he created man in his likeness, correct?)

2. God has always existed. He pervades time. He has always been and always will be.

3. There was a specific point in time that God created the universe.

Under Christian theology I think these are all true statements (I'm not a Christian so maybe I'm wrong).

My question is: What did God do before he created man?

Even if there were angels and demons or whatever before man there was still a specific point in time where God created them.

God sat around for literally and infinite number of years and just twiddled his thumbs? Waiting for what?

I was mulling this over last night, I'm pretty sure there is an error in my logic... let me know what you think...

ok, first of all, let's assume that there is a set of logical steps that we could use to prove the existence of a god. (let's also assume this isn't impossible)

now, using this same set of steps, but with slightly altered premises, could you not prove the existence of another god that was separate from the first god?

my point here is that the existence of one god, to me at least, seems to necessarily guarantee the existence of two gods, and three gods, and so on.

with this in mind, i've seen many monotheists search for "proof" of their gods existence. in my mind this seems silly. proof of one god would shatter all monotheistic institutions.

I guess my questions here are, where is my logic flawed (i'm assuming it is)? why are people so obsessed with proving to others that god exists? and what is your favorite type of candy?

have a nice day all :)

Give an example of subsets A and B in R^2 such that:

A and B are disconnected, but A ∪ B is connected.

Give an example of subsets A and B in R^2 such that:

A and B are connected, Cl(A) ∩ Cl(B) ≠ ∅, and A ∪ B is disconnected.

Let B ⊂ R^n be bounded in the Euclidean metric. Prove that the complement of B in R^n has exactly one unbounded component.

Let f : X ➝ Y be a homeomorphism.

Prove the following:

If S is a cutset f X, then f(S) is a cutset of Y.

Let X be a topological space.

Provide an example showing that the components of X are not necessarily open subsets of X.

Let X be a topological space. Show that each component of X is a closed subset of X.

Let X be a topological space. Prove that if A is connected in X, then A is a subset of some component of X.

Let Q be the set of rational numbers with the standard topology. Prove that Q is totally disconnected.

Prove that if if a topological space X has the discrete topology, then X is totally connected.

Let X and Y be topological spaces, and let X x Y be the corresponding product space. Define the projection functions

px = X x Y ➝ X and

py = X x Y ➝ Y

by px(x,y) = x and py(x,y) = y.

Prove that px and py are continuous.

Let (X,d) be a metric space. Show that for ε > 0 and x ∈ X, the closed ball Bd (x,ε) is the closure of the open ball Bd (x,ε).

This seems really trivial to me, but I'm having a hard time getting the notation right. Any help would be appreciated.

Also, I think I need to throw in the fact that x can't be an isolated point.

Let (X,d) be a metric space. Show that the closed balls in the metric d are closed sets in the topology on X induced by d.

Let K = {1/n ∈ Real #'s ⎮n ∈ positive integers}.

Show that the standard topology on K is the discrete topology.

I'm having a bit of trouble doing this with open balls... it should be really easy but i'm not getting it for some reason. Any help would be appreciated.

I'm trying to show that products of homeomorphic spaces are homeomorphic.

Let f : X ➝ Y and g : X' ➝ Y' be homeomorphisms. Prove that the function h : X × X' ➝ Y × Y', defined by h(x,x') = (f(x), g(x')), is a homeomorphism.

Let (x,d) be a metric space. Show that the closed balls in the metric d are closed sets in the topology on X induced by d.