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February 7th, 2019, 02:11 PM   #11
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There are n! natural number corresponding to n place digits
So there is 1 natural number corresponding to 1 place digit. I'm not sure what you mean by that or how it would relate, if at all, to your previous posts here. Can you specify the natural numbers you are referring to for n = 0, 1, 2 and 3?
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February 7th, 2019, 02:22 PM   #12
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Don't agonize over it if you didn't get the point right away. It's not that tight a post.
You're the only one agonizing over this stuff.

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Originally Posted by zylo View Post
There are n! natural number corresponding to n place digits, FOR ALL n.
Correction: There are $10^n$ whole numbers that may be represented using decimal notation across $n$ digits. E.g., there are $10^2 = 100$ numbers, 0 through 99, that may be represented using $n=2$ digits.

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There seems to be this notion floating around that if a sequence of digits is very large it can't be a natural number.
By definition, a sequence of digits isn't a natural number. The sum of $n$ terms of a sequence equates to a whole number when $n \in \mathbb{N}$ and the terms are all whole numbers.

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There is no ONE natural number at "infinity."
As you've been told time and time again, infinity is not a natural number. The ordinal $\omega$ is a limit ordinal, which is to say that it is a set containing all of the finite ordinals. There is no ordinal number $k$ such that $k < \omega$ and $k + 1 = \omega$. https://en.wikipedia.org/wiki/Ordinal_number

Is there a point to all of this? I think you may have officially lost it. It's as though you are regressing, which I didn't think was possible.

I find cranks fascinating. https://en.wikipedia.org/wiki/Crank_(person)

"The second book of the mathematician and popular author Martin Gardner was a study of crank beliefs, Fads and Fallacies in the Name of Science. More recently, the mathematician Underwood Dudley has written a series of books on mathematical cranks, including The Trisectors, Mathematical Cranks, and Numerology: Or, What Pythagoras Wrought. And in a 1992 UseNet post, the mathematician John Baez humorously proposed a checklist, the Crackpot index, intended to diagnose cranky beliefs regarding contemporary physics.[6]

According to these authors, virtually universal characteristics of cranks include:

1) Cranks overestimate their own knowledge and ability, and underestimate that of acknowledged experts.
2) Cranks insist that their alleged discoveries are urgently important.
3) Cranks rarely, if ever, acknowledge any error, no matter how trivial.
4) Cranks love to talk about their own beliefs, often in inappropriate social situations, but they tend to be bad listeners, being uninterested in anyone else's experience or opinions."

Last edited by AplanisTophet; February 7th, 2019 at 02:28 PM.
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February 7th, 2019, 02:38 PM   #13
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"The second book of the mathematician and popular author Martin Gardner . . . "
That needs correction. He wasn't a mathematician.
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February 7th, 2019, 05:49 PM   #14
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Originally Posted by zylo View Post
Don't agonize over it if you didn't get the point right away. It's not that tight a post.
You don't say/

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Originally Posted by zylo View Post
There seems to be this notion floating around that if a sequence of digits is very large it can't be a natural number.
Not everyone is as sloppy about formulating ideas as you may think.

What people are saying is that that no infinite sequence of decimal digits, except those that start with an infinite number of zeros, can be a "natural number" as usually defined.

It is not that people are being vague. It is that you do not bother to read carefully.

Last edited by skipjack; February 7th, 2019 at 07:50 PM.
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February 7th, 2019, 06:55 PM   #15
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Enough said.
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