My Math Forum  

Go Back   My Math Forum > College Math Forum > Topology

Topology Topology Math Forum


Reply
 
LinkBack Thread Tools Display Modes
May 28th, 2015, 10:04 AM   #11
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Quote:
Originally Posted by lemgruber View Post
I refer the statement what a straight is a curve with radius tends to infinite
Let's review what this means. You have a series of circles where the radius of the individual circles is increasing without bound. Perhaps the first circle has radius 1, the second radius 2, the third radius 3, and so on.

You could look at the curvature of each circle, for example, and find that it is 1 for the first, 1/2 for the second, 1/3 for the third, and so on. You could then note that the curvature of the sequence tends toward a limit, which is 0. This is what is means (formally) when a person says that as the radius increases without bound ("tends to $\infty$") that the curvature tends to 0.

What claim are you making about this sequence of circles? If you're defining a function f(C) is 1 if C is a curve and 0 otherwise, then f of the first circle is 1, f of the second circle is 1, and so on; the limit is, of course, 1.
CRGreathouse is offline  
 
May 28th, 2015, 12:15 PM   #12
Senior Member
 
Joined: Dec 2014
From: Brazil

Posts: 203
Thanks: 1

I say what the function when radius tends to ∞, not be defined in this point, that's all.


Lucio
lemgruber is offline  
May 28th, 2015, 01:09 PM   #13
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,618
Thanks: 2608

Math Focus: Mainly analysis and algebra
It doesn't have to be defined at the limit point for the limit to exist.
v8archie is offline  
May 28th, 2015, 01:26 PM   #14
Senior Member
 
Joined: Dec 2014
From: Brazil

Posts: 203
Thanks: 1

Forgive-me the error , I would to say the function not be defined when the radius tends to infinite, I wanna say it's limit doesn't exists what this occurs. What I say about the point, do not exist such thing like infinite point.

Lucio

Last edited by lemgruber; May 28th, 2015 at 01:28 PM.
lemgruber is offline  
May 28th, 2015, 02:13 PM   #15
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,618
Thanks: 2608

Math Focus: Mainly analysis and algebra
Well clearly the function is well defined for all finite radius. And in these cases the curvature is non-zero (positive, in fact). In the limit the curvature is zero, but the function is clearly 1.

It doesn't work to claim that the limit doesn't exist just because it doesn't say what you want it to say.
v8archie is offline  
May 28th, 2015, 02:20 PM   #16
Senior Member
 
Joined: Dec 2014
From: Brazil

Posts: 203
Thanks: 1

I agree.

Lucio
lemgruber is offline  
Reply

  My Math Forum > College Math Forum > Topology

Tags
circumference, depends, euclides, infinite, postulates



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
postulates/theorems Chanoch Geometry 2 April 29th, 2014 11:18 AM
Geometry postulates: confusion. rabbit Geometry 1 February 17th, 2012 10:06 PM
Probability of B if it depends on A happening or not peaceofmind Probability and Statistics 9 June 4th, 2011 06:40 PM
Postulates behind algebra? epson1 Algebra 13 February 21st, 2011 10:46 AM





Copyright © 2019 My Math Forum. All rights reserved.