Register to reply

Conway Base 13 Function

by LukeD
Tags: base, conway, function
Share this thread:
LukeD
#1
Jul25-08, 11:42 AM
P: 355
So I was browsing Wikipedia, and I stumbled across this article: http://en.wikipedia.org/wiki/Conway_base_13_function

The article claims that the Conway base 13 function, as a function from (0,1) to the reals is a counter example to the converse of the Intermediate Value Theorem (i.e., that for any a, b in (0,1) if f(a) < f(b), then for any c between f(a) and f(b), there is an x between a and b such that f(x) = c, but the function is not continuous)

The function sounds like it is very interesting; however, the article as written is very sparse and the definition of the function is not very clear to me. Maybe I'm misunderstanding the definition, but as it's written, it doesn't even seem to be a surjection to (0,1) though the article claims that it is.

Unfortunately, a google search of the function didn't bring anything up other than the wikipedia article. Is there anyone who understands this function who could give clear definition of it?
Phys.Org News Partner Science news on Phys.org
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history

Register to reply

Related Discussions
JH Conway Lecture General Math 0
Base One ? General Math 13
Base N to Base N Conversion Linear & Abstract Algebra 1
Acid-Base neutralization w/ more than 1 base. Chemistry 6
Why do we use base 10? General Math 6