## Search found 13 matches

Wed Jul 09, 2014 6:44 am UTC
Topic: 1392: "Dominant Players"
Replies: 187
Views: 38018

### Re: 1392: "Dominant Players"

The bit about Kira Zvorykina looks off. I think Randall probably meant 21st century, not 20th.
Fri Jun 14, 2013 2:37 am UTC
Forum: Mathematics
Topic: Cardinality of continua in ZF
Replies: 18
Views: 2052

### Re: Cardinality of continua in ZF

Apologies - I don't actually know the best method to solve the problem. I had assumed you would start with your space being a compact, Hausdorff, connected space which was countable, and then show that it actually wasn't one of those things. I had also assumed you would normally do that by invoking...
Fri Jun 14, 2013 2:14 am UTC
Forum: Mathematics
Topic: Cardinality of continua in ZF
Replies: 18
Views: 2052

### Re: Cardinality of continua in ZF

OK - but if you have an open cover of a countable, compact space, then you can always find a sub-cover that is finite, and use that, right? Or do you need Choice to find that sub-cover? (Edit: it does sound like you're saying that above, but since you only need to find finitely many elements of the...
Thu Jun 13, 2013 11:58 pm UTC
Forum: Mathematics
Topic: Cardinality of continua in ZF
Replies: 18
Views: 2052

### Re: Cardinality of continua in ZF

That make sense, thanks! But what if all of its members are countable? Surely all countable sets can be well-ordered without the Well-Ordering Theorem. They can, but you have to choose an enumeration of each of the members! OK, I think I'm finally getting it! Thanks for your patience Xenomortis too...
Thu Jun 13, 2013 9:32 pm UTC
Forum: Mathematics
Topic: Cardinality of continua in ZF
Replies: 18
Views: 2052

### Re: Cardinality of continua in ZF

dudiobugtron wrote:That make sense, thanks! But what if all of its members are countable? Surely all countable sets can be well-ordered without the Well-Ordering Theorem.

They can, but you have to choose an enumeration of each of the members!
Thu Jun 13, 2013 3:31 pm UTC
Forum: Mathematics
Topic: Cardinality of continua in ZF
Replies: 18
Views: 2052

### Re: Cardinality of continua in ZF

IANA set theorist, but I believe that would require some non-arbitrary way to map them to real numbers. For example, you could have an infinite set of collinear, equally-spaced points, which is countable, but enumerating them would require choosing one to start with, begging the question. Please no...
Thu Jun 13, 2013 2:29 pm UTC
Forum: Mathematics
Topic: Cardinality of continua in ZF
Replies: 18
Views: 2052

### Re: Cardinality of continua in ZF

I'm having trouble seeing why the axiom of countable choice isn't provable with just ZF. Can't you just use the well-ordering on the natural numbers to give you your choice function (by always choosing the element whose corresponding natural number is least)? Obviously I'm missing something - my gu...
Wed Jun 12, 2013 11:13 pm UTC
Forum: Mathematics
Topic: Cardinality of continua in ZF
Replies: 18
Views: 2052

### Cardinality of continua in ZF

A standard textbook theorem holds that in ZF + DC (Zermelo Fraenkel set theory with the axiom of dependent choice) every compact Hausdorff perfect space (perfect space=space with no isolated points) has at least the cardinality of the reals. A non-textbook-standard metrizability result that holds in...
Mon May 27, 2013 9:24 pm UTC
Topic: 1217: "Cells"
Replies: 57
Views: 25915

### Re: 1217: "Cells"

As for the chlorine bleach approach, I don't know how well it works to treat cancer, but I've managed to cure my psoriasis with it. There is some evidence that dilute sodium hypochlorite (bleach) is effective against plantar warts as well, but I sure wouldn't want to be in any drug trial involving ...
Mon May 27, 2013 8:12 am UTC
Topic: 1217: "Cells"
Replies: 57
Views: 25915

### Re: 1217: "Cells"

"Kills 99.9% of bacteria" - sure, so does soapy water. Only if it's antibacterial soap. Regular soapy water is good at washing bacteria away, but not great at killing them. At least, that's what I read on the internet somewhere. Indeed, but killing is somewhat overrated. Bacteria washed d...
Sun Dec 09, 2012 6:42 am UTC
Topic: 1144: Tags
Replies: 100
Views: 36978

### Re: 1144: Tags

<marquee><blink><strong>There is no shortage of ways to annoy people... Using <strong> appropriately is generally a good thing for accessibility. Using <marquee> or <blink> is punishable by eye-gouging in some jurisdictions. Regarding XHTML, why does anybody think readonly="readonly" is b...
Wed Sep 19, 2012 5:58 am UTC
Topic: 1110:"Click and Drag"
Replies: 595
Views: 665735

### Re: 1110:"Click and Drag"

I'd like to know if it's possible to get the whole image as one PNG. It appears to be a bunch of different ones stitched together with JS, and is quite tiring to navigate by touchpad.
Mon Aug 06, 2012 6:02 am UTC
Forum: Site/Forum issues
Topic: COPPA thingum--fixing an old account
Replies: 5
Views: 2598

### Re: COPPA thingum--fixing an old account

OP probably wants to re-use the name. Whatever the reason, one of the Chosen will see this and decide to fix it or not. Check back in occasionally. EDIT FOR SCIENCE: Check to see if dfeuer can post? I can't de-COPPA accounts without flipping through pages upon pages of crap, but I can add (non-COPP...