Re: Calculus XOR Probability

W. Dale Hall said:


Tony Orlow wrote:

... stuff deleted ...

There were a bunch of sidebars Rusin introduced. I wasn't going to be
distracted in every direction, but was trying to address certain things. Here,
I think he means ....363636 is 4/3 as large as ...272727. Given the same
infinite of digits, this is true.


Presumably, you mean 'given the same infinity of digits'.

Nice typo catch.


However, the digits have a 1:1 correspondence with the natural numbers.

Not necessarily. If they are both 100 digits long, it's true too.


Therefore (according to you) there are only finitely many digits. In
fact, you should be claiming that there are *fewer* digits than there
are natural numbers.

I have no problem with infinite strings of digits. The finiteness of the
natural numbers, which doesn't particularly have any bearing on these adic
numbers, derives from the identity relation between element count and value in
the set, and the restriction of finiteness imposed on the values.


You really should get your terminology under control.

Yeah, thanks.


BTW, it seems like you *still* haven't solved the problem of

"everything is divisible by x"

for *every* natural number x coprime to 10. There's no getting around
this for your version of the integers. I've already shown you how to
do that division, so you can't claim it ain't so.

Shouldn't that be an important issue? After all, what use are your
numbers if you can't even do arithmetic? If your numbers are of no
use (i.e., literally "useless"), then aren't they worthless?

Hi Dale. Been a long time. So long, it appears, that you don't seem to recall
the lengthy response I gave to your "everything is divisible by 7" argument,
where I fully analyzed what you were doing, and confirmed that, with the 10-
adics, indeed ...110, ...111, ...112, etc are apparently divisible by 7. I
explained why this was so, pointed out that in fact ...1115 is NOT divisible by
7, since there is no multiple of 7 consisting of a string of 1's ending in a 5
as is true for the other 9 digits, and finally, reminded you that my infinite
number system is distinctly different from the adics. They're not "left-
infinite", but "center-infinite". I then applied the division by 7 to my unit
infinity, 1:000...000, and found that, with a six-digit repeating sequence in
decimal 1/7, the remainder of dividing decimal infinity by 7 could be any of
six different values, from 1 through 6, and could not be 0, which makes sense,
since no power of 10 could be evenly divisible by 7. So, I showed that my
numbers work there the adics don't.

So, you can claim that I never solved your "problem", that arithmetic doesn't
work with the T-riffic numbers, and that my ideas are worthless, but that's a
bunch of baloney, and if you have any memory of the response which I describe
and a shred of integrity, then you'll admit that I exposed your tricky
maneuver, which I don't think you invented, and that the objection was vacuous
and irrelevant. Okay?


Dale.


--
Smiles,

Tony
.

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