My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


Thanks Tree17Thanks
Closed Thread
 
LinkBack Thread Tools Display Modes
September 19th, 2018, 02:17 PM   #1
Senior Member
 
Joined: Jun 2018
From: UK

Posts: 103
Thanks: 1

Infinity

Set theory uses the ‘axiom of infinity’ which is equivalent to ‘actual infinity exists’. I believe this axiom is wrong - Actual Infinity cannot exist:

Numerically:

- There is no natural number with the property that repeatedly subtracting one from it never reaches zero
- Hence Actual Infinity is not a number.
Or
- Actual Infinity is larger than any other number
- Actual infinity plus one is larger than infinity
- Hence there is no number larger than all other numbers

Geometrically:

- It is impossible to construct a line segment with the property that it is longer than all other line segments

Temporally:

- Assume infinite time
- so anything than can possibly happen will eventually happen
- If it happens once it will eventually happen again
- So it will eventually happen an infinite number of times
- no matter how unlikely it was in the first place
- But is this not absurdity?

Paradoxes are solved:

- Zeno’s paradoxes. It’s impossible to travel any distance as movement requires an infinite number of steps. We can move. Reductio ad absurdum. Space must be discrete

- Galileo's paradox is solved:
- There are less squares than numbers because not all numbers are squares. Yet each number has a square so the number of numbers and squares must be the same.
- He is trying to compare two actually infinite sets, IE comparing two undefined things. A set definition is not complete until all its members are iterated.

- Hilbert’s infinite hotel paradox is solved; such a hotel cannot exist.

Common sense View:

The Actually Infinite exists. Reductio ad absurdum. No it doesn’t.

This is surely the only possible conclusion for those with a materialistic view of the world; materialism and the Actually Infinite do not mix.
Devans99 is offline  
 
September 19th, 2018, 02:39 PM   #2
Global Moderator
 
Joined: May 2007

Posts: 6,641
Thanks: 625

You are making too much of it. Mathematicians prefer to use the term becomes infinite, rather than goes to infinity, so that for example, to resolve Zeno's paradox, you don't stop the process after a finite number of steps.
mathman is offline  
September 19th, 2018, 02:55 PM   #3
Senior Member
 
Joined: Jun 2018
From: UK

Posts: 103
Thanks: 1

I am not making too much of it: Actual Infinity does not exist implies time has a start which is interesting...
Devans99 is offline  
September 19th, 2018, 04:00 PM   #4
Math Team
 
topsquark's Avatar
 
Joined: May 2013
From: The Astral plane

Posts: 1,915
Thanks: 774

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by Devans99 View Post
I am not making too much of it: Actual Infinity does not exist implies time has a start which is interesting...
Just because we can't physically construct something does not mean it can't exist. Mathematics constructions are not physical so why should we base the existence of infinity (which, yes, is not a number) on a physical basis? We can't construct the exact value of $\displaystyle \pi$ by measuring the circumference and diameter of a circle. So do we say that $\displaystyle \pi$ does not exist?

Besides, the Axiom of Infinity is an axiom... Axioms are assumed statements that are useful for the basis of a construction. They are neither provable nor unprovable.

-Dan
topsquark is offline  
September 19th, 2018, 04:09 PM   #5
Senior Member
 
Joined: Jun 2018
From: UK

Posts: 103
Thanks: 1

But you can’t numerically or geometrically construct Actual Infinity.

If it can’t be constructed physically or mathematically and does not exist in nature then it does not exist.

Got to be the worst axiom in history...
Devans99 is offline  
September 19th, 2018, 05:02 PM   #6
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,511
Thanks: 2514

Math Focus: Mainly analysis and algebra
Quote:
Originally Posted by Devans99 View Post
- There is no natural number with the property that repeatedly subtracting one from it never reaches zero
- Hence Actual Infinity is not a number.
Or
- Actual Infinity is larger than any other number
- Actual infinity plus one is larger than infinity
- Hence there is no number larger than all other numbers
- It is impossible to construct a line segment with the property that it is longer than all other line segments
You are confusing all manner of different "infinities". In fact, mathematics doesn't define "infinity". Instead there are several different types of infinite objects. Infinite sets are one such object - although they are actually sets having transfinite cardinality and there are various transfinite numbers. These are not natural numbers, and so no, you can't subtract 1 from them any number of times to get zero.

However, there are many types of number that you can't subtract 1 from to get zero: "most" of the rationals for example.

The axiom of infinity effectively only says (to me) that it is reasonable to talk about "the natural numbers" as a set. It doesn't make any claims about either natural numbers themselves or transfinite numbers.
v8archie is offline  
September 19th, 2018, 05:12 PM   #7
SDK
Senior Member
 
Joined: Sep 2016
From: USA

Posts: 520
Thanks: 293

Math Focus: Dynamical systems, analytic function theory, numerics
Quote:
Originally Posted by Devans99 View Post
But you can’t numerically or geometrically construct Actual Infinity.

If it can’t be constructed physically or mathematically and does not exist in nature then it does not exist.

Got to be the worst axiom in history...
Almost every single thing in your OP is completely wrong, often in multiple ways. However, this comment is the most egregious.

I also can't remove every molecule of gasoline from my car's gas tank. Thus by your logic I should stop gassing it up because I can't run out.

If you want to do math, I suggest you start by spending some time reading about it.
SDK is offline  
September 19th, 2018, 05:50 PM   #8
Math Team
 
topsquark's Avatar
 
Joined: May 2013
From: The Astral plane

Posts: 1,915
Thanks: 774

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by Devans99 View Post
But you can’t numerically or geometrically construct Actual Infinity.

If it can’t be constructed physically or mathematically and does not exist in nature then it does not exist.

Got to be the worst axiom in history...
Who says Mathematics has to be taken as the image of the real world?

Infinity: The distance from the origin to where two parallel lines meet.

Infinity: The number of ways to circle the globe and get back to your original position.

Infinity: The time spent trying to get the pretty girl at the bar to notice you.

Infinity: The number of possible ways that two electrons can interact in QED.

I'm sure we can come up with more.

To infinity! And beyond!

-Dan
topsquark is offline  
September 19th, 2018, 06:40 PM   #9
Senior Member
 
Joined: Jun 2018
From: UK

Posts: 103
Thanks: 1

Quote:
Originally Posted by SDK View Post
Almost every single thing in your OP is completely wrong, often in multiple ways. However, this comment is the most egregious.

I also can't remove every molecule of gasoline from my car's gas tank. Thus by your logic I should stop gassing it up because I can't run out.

If you want to do math, I suggest you start by spending some time reading about it.
- You can remove every molecule theoretically and approximately.
- But you can’t construct actual infinity either theoretically or approximately (in a finite number of steps)

Surely this tells us something; you’re gas tank is real and Actual Infinity is not
Devans99 is offline  
September 19th, 2018, 06:47 PM   #10
Senior Member
 
Joined: Jun 2018
From: UK

Posts: 103
Thanks: 1

Quote:
Originally Posted by topsquark View Post
Who says Mathematics has to be taken as the image of the real world?

Infinity: The distance from the origin to where two parallel lines meet.

Infinity: The number of ways to circle the globe and get back to your original position.

Infinity: The time spent trying to get the pretty girl at the bar to notice you.

Infinity: The number of possible ways that two electrons can interact in QED.

I'm sure we can come up with more.

To infinity! And beyond!

-Dan
But mathematics is used to model the real world and so is Actual Infinity.

You do not have enough graph paper for your parallel lines example to work in the real world.

You lack a truely continuous surface on which to realise your globe example.

There are no examples of Actually Infinite in the natural world.
Devans99 is offline  
Closed Thread

  My Math Forum > High School Math Forum > Elementary Math

Tags
infinity



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Sum to infinity matisolla Calculus 3 February 6th, 2015 08:36 PM
Infinity. deanmullen10 Applied Math 10 July 30th, 2010 02:18 AM
Solve X where -infinity>x>infinity -DQ- Algebra 5 September 14th, 2009 06:13 AM
infinity fibonaccilover Applied Math 9 July 26th, 2009 09:07 PM
Infinity... nerd9 Number Theory 1 December 31st, 1969 04:00 PM





Copyright © 2018 My Math Forum. All rights reserved.