Thanks. I guess I agree with the your quale and betting
descriptions. Finiteness is an existence statement, there exists an
end. If we are talking about an actual particular group of things, we
need an observer to say where the end is, thus declaring it to be
finite. But it is another thing
Le 14-juil.-06, à 18:52, Tom Caylor a écrit :
Here is where I believe the crux is: ... means you can continue to
add the I as many times as you want. Actually, this is equivalent
to: ... means you can continue to add the I as many times as you
want and you can. It's just a little
Hi Quentin, Tom and List,
Of course, N is the set of finite positive integers:
N = {0, 1, 2, 3, ...}.
An infinite set A is countable or enumerable if there is a computable bijection between A and N.
Forgetting temporarily the number zero, all finite number can be put in the shapes:
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Le 14-juil.-06, à 14:34, Bruno Marchal a écrit :
Hi Quentin, Tom and List,
Of course, N is the set of finite positive integers:
N = {0, 1, 2, 3, ...}.
An infinite set A is countable or enumerable if there is a computable
bijection between A and N.
Please suppress the computable in
Hi, thank you for your answer.But then I have another question, N is usually said to contains positive integer number from 0 to +infinity... but then it seems it should contains infinite length integer number... but then you enter the problem I've shown, so N shouldn't contains infinite length
Quentin Anciaux wrote:
Hi, thank you for your answer.
But then I have another question, N is usually said to contains positive
integer number from 0 to +infinity... but then it seems it should contains
infinite length integer number... but then you enter the problem I've
shown,
so N shouldn't
N is defined as the positive integers, {0, 1, 2, 3, ...}, i.e. the
*countable* integers. (I am used to starting with 1 in number
theory.) N does not include infinity, neither the countable infinity
aleph_0 nor any other higher infinity. Infinite length integers
fall into this category of
Technically, I should say that countable means that the set can be put
into a one-to-one correspondence with *a subset of* N, to include
finite sets.
Tom
Tom Caylor wrote:
N is defined as the positive integers, {0, 1, 2, 3, ...}, i.e. the
*countable* integers. (I am used to starting with 1
Hi list,
I have a question I've been thinking about for a while... It may seems stupid,
but I need to understand where I'm wrong.
So here it is... Does the set N contains infinite number ?
I ask this because Cantor prove with the diagonalisation argument that the set
R is uncountable and
I think my easy answer is to say that infinite numbers are not in N. I
like to think of it with a decimal point in front, to form a number
between 0 and 1. Yes you have the rational numbers which eventually
have a repeating pattern (or stop). But you also have in among them
the irrational
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