Register to reply

There exists one number N

by arbol
Tags: exists, number
Share this thread:
arbol
#1
Mar27-08, 02:04 PM
P: 50
The set N of natural numbers = {1, 2, 3, 4, ...}.

But there exists one (1) number N, such that

N = 12345678910111213... (where the unit's place is at infinity).

A good example of an irrational number then would be

1.234567891011121314...
Phys.Org News Partner Science news on Phys.org
New type of solar concentrator desn't block the view
Researchers demonstrate ultra low-field nuclear magnetic resonance using Earth's magnetic field
Asian inventions dominate energy storage systems
belliott4488
#2
Mar27-08, 02:06 PM
belliott4488's Avatar
P: 666
Quote Quote by arbol View Post
N = 12345678910111213... (where unit's place is at infinity).
Doesn't that make N = infinity?
mathwonk
#3
Mar27-08, 04:09 PM
Sci Advisor
HW Helper
mathwonk's Avatar
P: 9,470
so, put a decimal in front of it.

oh he did that.

HallsofIvy
#4
Mar27-08, 05:13 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,489
There exists one number N

Quote Quote by arbol View Post
The set N of natural numbers = {1, 2, 3, 4, ...}.

But there exists one (1) number N, such that

N = 12345678910111213... (where the unit's place is at infinity).
No, there is no such number. All integers have only a finite number of digits. By the way, it is not at all a good idea by using "N" to represent the set of natural numbers and then say that "N" is a number.

A good example of an irrational number then would be

1.234567891011121314...
Now THAT is a perfectly good irrataional number.
Hurkyl
#5
Mar27-08, 06:05 PM
Emeritus
Sci Advisor
PF Gold
Hurkyl's Avatar
P: 16,091
Quote Quote by arbol View Post
But there exists one (1) number N, such that

N = 12345678910111213... (where the unit's place is at infinity).
Are you sure that decimal string actually denotes a number? How can the unit's place be 'at infinity'? What digit is in the unit's place?
CRGreathouse
#6
Mar27-08, 07:36 PM
Sci Advisor
HW Helper
P: 3,684
Quote Quote by arbol View Post
A good example of an irrational number then would be

1.234567891011121314...
That's 10 times Champernowne constant.
HallsofIvy
#7
Mar28-08, 06:54 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,489
If it were possible to construct any irrational number by putting a decimal into some positive integer, that would imply that the set of irrational numbers is countable.
arbol
#8
Mar28-08, 01:23 PM
P: 50
Quote Quote by Hurkyl View Post
Are you sure that decimal string actually denotes a number? How can the unit's place be 'at infinity'? What digit is in the unit's place?

good question
arbol
#9
Mar28-08, 01:24 PM
P: 50
Quote Quote by HallsofIvy View Post
No, there is no such number. All integers have only a finite number of digits. By the way, it is not at all a good idea by using "N" to represent the set of natural numbers and then say that "N" is a number.


Now THAT is a perfectly good irrataional number.
It is necessary that N is not an interger, but it is one number.
arbol
#10
Mar28-08, 01:25 PM
P: 50
Quote Quote by HallsofIvy View Post
No, there is no such number. All integers have only a finite number of digits. By the way, it is not at all a good idea by using "N" to represent the set of natural numbers and then say that "N" is a number.


Now THAT is a perfectly good irrataional number.
you can call it anything you want
arbol
#11
Mar28-08, 01:27 PM
P: 50
Quote Quote by belliott4488 View Post
Doesn't that make N = infinity?
lim f(x) (as x approaches infinty) is infinity, but N is a single number (not a variable).
arbol
#12
Mar28-08, 01:32 PM
P: 50
Quote Quote by HallsofIvy View Post
If it were possible to construct any irrational number by putting a decimal into some positive integer, that would imply that the set of irrational numbers is countable.
a definition of an irrational number is a number that cannot be expressed in the form m/n, where m and n are intergers and n not equal to zero. such numbers are infinite to right of the decimal point and do not repeat. for example,

1.234567891011...
CRGreathouse
#13
Mar28-08, 01:57 PM
Sci Advisor
HW Helper
P: 3,684
Quote Quote by arbol View Post
a definition of an irrational number is a number that cannot be expressed in the form m/n, where m and n are intergers and n not equal to zero. such numbers are infinite to right of the decimal point and do not repeat.
Yes, so together with Hallsofivy's statement you know that 123456789101112... is not an integer.
ramsey2879
#14
Mar28-08, 06:01 PM
P: 894
Quote Quote by arbol View Post
It is necessary that N is not an interger, but it is one number.
All Numbers must have a meaning such that a rational number can be found to approximate the number within a chosen value, a expression that is an infinite string of numbers without any fixed decimal point does not have any meaning and is not a number.
HallsofIvy
#15
Mar30-08, 06:39 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,489
Quote Quote by arbol View Post
good question
Yes it was. Since it was about your post, do you have a good answer?

Quote Quote by arbol View Post
It is necessary that N is not an interger, but it is one number.
Okay, what do you mean by "number". And my criticism was simply about using the same symbol, N, with two different meanings.

Quote Quote by arbol View Post
you can call it anything you want
Thank you. But I do prefer to use standard terminology. If you did that, it might be easier to understand what you are trying to say.

Quote Quote by arbol View Post
lim f(x) (as x approaches infinty) is infinity, but N is a single number (not a variable).
??This is the first time you mentioned "f(x)". Where did that come from. Once again, the N you posit is NOT a "number" by any standard definition.

Quote Quote by arbol View Post
a definition of an irrational number is a number that cannot be expressed in the form m/n, where m and n are intergers and n not equal to zero. such numbers are infinite to right of the decimal point and do not repeat. for example,

1.234567891011...
Yes, we know that- it is not necessary to state the obvious.
arbol
#16
Mar31-08, 04:53 PM
P: 50
Quote Quote by belliott4488 View Post
Doesn't that make N = infinity?
Yes. I think it does.

If f(x) = x, then

lim (of f(x) as x approaches infinity) = infinity = N. (but the unit's place of N is at infinity.)


CRGreathouse
#17
Mar31-08, 06:12 PM
Sci Advisor
HW Helper
P: 3,684
But since "infinity" is not an integer, you know that N isn't an integer.
LorenzoMath
#18
Apr2-08, 09:39 AM
P: 41
1234567891011... is not a conventional way of representing real numbers, so unless you introduce your own convention, it doesn't mean anything. Whereas if you put a disimal point somewhere, it represents a real number in a conventional sense. Because, by convention, 1.234567... represents some real number to which the sequence, 1, 1.2, 1.23, 1.234, ... converges. This is what we call the completeness of R. If we agree to say that 1234567891011... represents where the sequence 1, 12, 123, 1234, ... go, then we may call it infinity, or more precisely, we introduce the concept of infinity.


Register to reply

Related Discussions
Proving that a real number exists in between a real number, Calculus 19
I need to know if this exists Advanced Physics Homework 2
God exists ?! General Discussion 100
Therefore God Exists General Discussion 2
Does God Exists? General Discussion 40