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tech / sci.math / Re: Integers

SubjectAuthor
* IntegersEarle Jones
+- Re: Integerssergio
+- Re: IntegersJim Burns
`- Re: IntegersFromTheRafters

1
Integers

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From: earle.jo...@comcast.net (Earle Jones)
Subject: Integers
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 by: Earle Jones - Wed, 27 Apr 2022 03:45 UTC

*
Do you believe this?

If, there exists an integet n then there exists an integer n + 1?

earle
*

Re: Integers

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From: inva...@invalid.com (sergio)
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Subject: Re: Integers
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 by: sergio - Wed, 27 Apr 2022 16:12 UTC

On 4/26/2022 10:45 PM, Earle Jones wrote:
> *
> Do you believe this?
>
> If, there exists an integet n then there exists an integer n + 1?
>
> earle
> *

perhaps, if I believed in the + sign too.

Re: Integers

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From: james.g....@att.net (Jim Burns)
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Subject: Re: Integers
Date: Wed, 27 Apr 2022 14:12:33 -0400
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 by: Jim Burns - Wed, 27 Apr 2022 18:12 UTC

On 4/26/2022 11:45 PM, Earle Jones wrote:

> Do you believe this?
>
> If, there exists an integet n
> then there exists an integer n + 1?

Yes, because
that is an important part of
what we mean by "integer".

It is a question similar to
| | Does there exist a unicorn without a horn in
| the middle of its forehead?

It's different in nature from
| | Is there a unicorn standing in my garden?

No unicorns in my garden doesn't
change what we mean by "unicorn".

And the forehead-horn doesn't really address
whether actual, real unicorns exist.
It's more about how we would know if
we'd met a unicorn. Hypothetically.

> If, there exists an integet n
> then there exists an integer n + 1?

Yes, because that's part of what "integer" means.

----
It's extremely important to the way we reason about
infinitely-many integers that we have claims
which we know is true for an integer
_even if we *don't know* which integer_

We can start with a claim about n like that and maybe
a few more. And then we can find another claim about n
which _must_ be true if the already-known claims
are true. And then another claim. And then another claim.
At each step, we have another claim which we know
is true without knowing which integer n is.

We don't interact with each integer.
We can't, we're finite beings.

However, we don't need to interact with each integer n
in order to now that n+1 exists -- and to know
many more things about each integer.

Re: Integers

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Integers
Date: Wed, 27 Apr 2022 13:41:11 -0700
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 by: FromTheRafters - Wed, 27 Apr 2022 20:41 UTC

Earle Jones explained :
> *
> Do you believe this?
>
> If, there exists an integet n then there exists an integer n + 1?
>
> earle
> *

Are you starting from scratch? With induction? I'm wondering what you
are getting at.

Certainly, if 'n' is a natural number, then the successor to 'n' is
also. The naturals are embedded in the integers, so the inverse
successor function on the naturals should work (with closure) on the
integers.

Each integer has a plus one and a minus one guaranteed.

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