## Sunday, March 02, 2008

### The Compliment of an Open set

My question to you: what is the compliment of an open set?

You might want to think very carefully about this one. Don't panic--it's not a race to the finish line. Take deep breaths before answering the question: I won't shout at you if you get it wrong! (Not that that ever frightens anyone).

#### 6 comments:

steve said...

Before answering the question readers might like to think about the difference between compliment and complement.

I can pay you a compliment or tell you what the complement of an open set is. :)

Beans said...

Aah--nothing gets past you Steve!! :D

(You didn't have to give the game away though!) *cue sad face*

I still wouldn't mind hearing what people's initial answer to that question was.

Hmmm, paying me a compliment sounds nicer so go for it. Haha, only kidding. In my complex analysis notes I made the mistake of writing "i" and the lecturer (unable to hold his laughter might I add) corrected me during the example class.

I thought it was my duty to other maths students, to save them from similar embarrassment!

steve said...

Whoops! I just thought you had made a spelling mistake - I didn't realise that was the point of the question. Sorry!

You are welcome to remove my comment to see what others say.

Beans said...

It's OK, I doubt anyone else will say anything, so there's no harm in having the correct answer posted. (It was meant to be a trick question. :p)

Although me making a spelling mistake seems a very likely thing, for I did make the error initially.

jd2718 said...

The complement of an open set?
Hmm. Should it be "not open?"
Example: a disk: its
Edge belongs to the complement
More examples?
Perhaps we need to look elsewhere.
The plane, it is open?
Yes.
So what would its complement be?
Eh?
That's enough.

Jonathan

Beans said...

Hi Jonathan,

"Eh" is precisely what is going through my head at the moment, but my excuse is that its 1am!

What's another word for "not open", is what I had in mind.

Hmm, interesting final point you made there. I do recall something like that being mentioned in my notes (which I need to read over).

Or, if I may continue my inane ramble, should it be phrased "a set is closed if..."?