skipjack

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?

AplanisTophet

You're the only one agonizing over this stuff.

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.

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.

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."

skipjack

That needs correction. He wasn't a mathematician.

JeffM1

You don't say/

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.

greg1313

Enough said.