My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 5th, 2013, 12:23 AM   #1
Newbie
 
Joined: Dec 2010

Posts: 8
Thanks: 0

Infinite set of numbers

If you pick n (n > 0) numbers at random from infinite set (say positive whole numbers) what is the probability you pick a specific number (1 for example)? The question bothers me because from one side it seems the probability must be greater than 0 (since some numbers are being picked), but from other side it seems that the probability is zero since the set is infinite.
Thanks in advance
kustrle is offline  
 
February 5th, 2013, 12:52 AM   #2
Math Team
 
mathbalarka's Avatar
 
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Infinite set of numbers

Such probability is not possible to calculate assumed that probability of picking every integer is the same. Say the probability you picked any integer N is P(N). Since the probability of picking every integer is the same, P(N)=k. Sum of the probabilities of picking each and every integer is 1 -- P(1) + P(2) + . . . = 1, hence k + k + k + . . . = 1 which is impossible for any positive real number k. Hence, the probability doesn't exists.
mathbalarka is offline  
February 5th, 2013, 05:15 AM   #3
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 933

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Infinite set of numbers

There is no uniform distribution on a countably infinite set; your question contains an assumption which is not true.
CRGreathouse is offline  
October 18th, 2015, 10:40 AM   #4
Newbie
 
Joined: Oct 2015
From: India

Posts: 2
Thanks: 0

You first have to understand the meaning of infinite... Infinite in maths is like beyond boundary ... If you can think only to 99 ... 100 is infinite for you.. So it is not define what no. Are included... Probably probability only apply to definite things Bcoz it is based on tries and success.

Last edited by skipjack; October 18th, 2015 at 11:32 AM.
Hardik is offline  
October 18th, 2015, 12:29 PM   #5
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,937
Thanks: 2265

Math Focus: Mainly analysis and algebra
Hardik's comment is false. The Poisson and Geometric distributions comfortably handle the infinite within a discrete probability space. The Normal distribution does so in a continuous space. These are only examples - there are infinitely many distributions that do the same.

But any discrete distribution that handles the infinite must have $\Pr{(X=x)}\to 0$ as $x \to \infty$, and any continuous distribution must have $\Pr{(X\gt x)}\to 0$ as $x \to \infty$. This is because the cumulative probability distribution function must tend to unity.
v8archie is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
infinite, numbers, set



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Relation between an infinite product and an infinite sum. Agno Number Theory 0 March 8th, 2014 04:25 AM
Prove that there exist infinite Composite numbers mathcool Number Theory 3 December 9th, 2011 05:25 AM
infinite cardinal numbers xianghu21 Applied Math 0 March 24th, 2010 09:18 AM
Infinite sum of the reciprocals of the Fibonacci numbers. Infinity Number Theory 13 July 21st, 2007 08:35 PM
Drawing infinite numbers of lines Infinity Applied Math 4 July 3rd, 2007 06:19 PM





Copyright © 2017 My Math Forum. All rights reserved.