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factorial base

Type of Math Object: 
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Mathematics Subject Classification

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Can you offer either a theorem and proof, or examples
that make this claim clear?

"The factorial base representations are unambiguous as long as the maximum allowed digit for a given place value is not exceeded (e.g., the least significant digit can only be 0 or 1, while the most significant digit in an 7-digit factorial base number has to be in the range 0 to 7). Thus factorial base has the potential to use an infinite amount of distinct digits even as the less significant place values are limited in what values they can contain."

For 7 you can write 101 ( = 1*3!+0*2!+1*1!) or 31 ( = 3*2!+1*1!), but with the second representation you've exceeded the maximum allowed digit in the two-factorial place-value. Doesn't get any clearer than that.

P.S. What's the longest proof that 1 + 1 = 2?

I think you would be wiser to listen to "jac"'s suggestion and rewrite that paragraph. It is not clear to me either and many other users will find it difficult to read. On the other hand, the fact that any number can be represented uniquely in a factorial base is no trivial fact, and a proof of this fact would be a nice addition to the entry.


Sniff... Torquemada: could you please pay attention to who wrote what?

Lando: Could you not write in that way that makes people like Torquemada think I said something I didn't actually say?

Its all gonna have to wait until after Memorial Day anyway.

> Sniff... Torquemada: could you please pay attention to who
> wrote what?

My mistake, sorry. However, "jac" did rise a legitimate point. The paragraph could be clearer in exposition, and a proof of that fact would be extremely helpful to the reader.


Lisa, I'm sorry that my remarks caused others to lash out at you.

I still think that the article is clear enough, but then again, I understand written English better than native speakers. My suggestion: clarify by obfuscating. Find some way to put x amount of Greek letters into the page. That should do the trick.


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