Does Anyone Understand the Conway Base 13 Function?

In summary, the conversation discusses an article on Wikipedia about the Conway base 13 function, which is claimed to be a counter example to the converse of the Intermediate Value Theorem. The article is sparse and the definition of the function is unclear. The function may not even be a surjection to (0,1). A Google search did not yield any further information, but a paper with a clearer definition is provided.
  • #1
LukeD
355
3
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?
 
Last edited:
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  • #2
Here is a more elaborated paper:
https://www.uccs.edu/Documents/goman/Converse%20of%20IVT.pdf
 

FAQ: Does Anyone Understand the Conway Base 13 Function?

What is the Conway Base 13 Function?

The Conway Base 13 Function is a mathematical function developed by mathematician John H. Conway. It is used to convert numbers from base 10 (decimal) to base 13 (tridecimal).

How does the Conway Base 13 Function work?

The function works by breaking down a number into its individual digits and multiplying each digit by its corresponding power of 13. The resulting products are then added together to get the final converted number in base 13.

Why use base 13 instead of the more commonly used base 10?

Base 13 allows for a more efficient and concise representation of numbers compared to base 10. This can be beneficial in certain mathematical calculations and can also be used for encryption purposes.

Are there any limitations to the Conway Base 13 Function?

One limitation is that the function only works for positive integers. It also may not be suitable for complex mathematical operations and is primarily used for converting numbers between base 10 and base 13.

How is the Conway Base 13 Function useful in real-world applications?

The function has been used in various fields such as computer science, cryptography, and game theory. It can also be used in everyday life for tasks such as creating unique identification numbers or encoding data for secure communication.

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