Share this thread: 
#1
Mar2708, 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... 


#3
Mar2708, 04:09 PM

Sci Advisor
HW Helper
P: 9,488

so, put a decimal in front of it.
oh he did that. 


#4
Mar2708, 05:13 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,565

There exists one number N



#5
Mar2708, 06:05 PM

Emeritus
Sci Advisor
PF Gold
P: 16,091




#6
Mar2708, 07:36 PM

Sci Advisor
HW Helper
P: 3,684




#7
Mar2808, 06:54 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,565

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.



#8
Mar2808, 01:23 PM

P: 50

good question 


#9
Mar2808, 01:24 PM

P: 50




#10
Mar2808, 01:25 PM

P: 50




#11
Mar2808, 01:27 PM

P: 50




#12
Mar2808, 01:32 PM

P: 50

1.234567891011... 


#13
Mar2808, 01:57 PM

Sci Advisor
HW Helper
P: 3,684




#14
Mar2808, 06:01 PM

P: 894




#15
Mar3008, 06:39 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,565




#16
Mar3108, 04:53 PM

P: 50

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.) 


#17
Mar3108, 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.



#18
Apr208, 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 