My Math Forum Infinite Decimal is a Natural Number

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June 4th, 2016, 06:26 AM   #21
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Quote:
 Originally Posted by zylo Why won't you answer it?
Why have you not answered any of the questions and points that have been put to you? Why should anyone answer your question when you refuse to answer those of others.

June 4th, 2016, 07:35 AM   #22
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Quote:
 Originally Posted by v8archie Why have you not answered any of the questions and points that have been put to you? Why should anyone answer your question when you refuse to answer those of others.
Your and skipjack's replies are mathematically vaque, ambiguous, and rambling. I can't find any specific questions. My question is mathematically precise and requires only a yes or no answer:

1) Is 3333.. to n places a natural number for all n? Yes or no please.

You use the term "infinite" to describe the sequence of 3's in .333333.....
2) What is your definition of infinite?

June 4th, 2016, 09:47 AM   #23
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Quote:
 Originally Posted by zylo I can't find any specific questions.
Do you not know what a question looks like then? There are loads of questions directed at you, mostly from skipjack. I have asked some questions and given mathematical demonstrations as to why your ideas are incorrect which you have made no attempt to refute.

Quote:
 Originally Posted by zylo 1) [U]Is 3333.. to n places a natural number for all n?
I answered this earlier today. But the answer doesn't mean what you want it to, because of your misunderstanding of the term "for all $n$". Your question is rendered imprecise by your usage of "for all $n$".

Quote:
 Originally Posted by zylo 2) What is your definition of infinite?
I have given precise mathematical definitions of finite and infinite in terms of sets and sequences. It's easy to formulate a similar definition for decimals, but I'm not going to waste my effort doing it here. Informally, you may take it as a synonym for "non-terminating".

Your suggestion that skipjack and I have been vague and ambiguous shows that you don't understand the posts. Rather than writing them off, you should seek clarification. The reason you don't do that is because you know that they show your own ideas to be worthless nonsense.

Last edited by skipjack; June 4th, 2016 at 09:53 PM.

June 4th, 2016, 11:59 AM   #24
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Is 3333.. to n places a natural number for ALL n?

Quote:
 Originally Posted by v8archie ...., as you have been told many, many, many times before "for all $n$" includes only finite values of $n$......
My apologies. You did answer my question: yes.
Thanks

A finite set of natural numbers has an upper bound. The set of all natural numbers, though consisting only of finite numbers, has no upper bound, and is countable, just like 333...to n places is a natural number for all n.

So you are relying on your past definition of infinite,
non-finite and non-countably infinite?
A cow is infinite.

June 4th, 2016, 12:12 PM   #25
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Quote:
 Originally Posted by zylo A finite set of natural numbers has an upper bound. The set of all natural numbers, though consisting only of finite numbers, has no upper bound, and is countable
All of this is true. There exist arbitrarily large natural numbers, but all of them are finite.

Quote:
 just like 333...to n places is a natural number for all n.
This also is true for finite $n$.

However, the infinite (non-terminating) sequence of 3s 333... is not a natural number as I demonstrated previously.

Quote:
 A cow is infinite.
Don't be stupid. If you don't understand, say so and I might try to help... if you haven't exhausted my patience.

June 4th, 2016, 11:55 PM   #26
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Quote:
 Originally Posted by zylo . . . I can't find any specific questions.

Quote:
 Originally Posted by zylo 1) Is 3333.. to n places a natural number for all n?
Yes, for each n, but each natural number is finite, so 3333... (non-terminating) isn't a natural number and there is no natural number n that gives how many digits 3333... has.

Hence it doesn't follow that the reals are countable.

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