The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Uncountability of the Real Numbers Without Decimals
Replies: 110   Last Post: Dec 10, 2013 4:33 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
gnasher729

Posts: 419
Registered: 10/7/06
Re: Uncountability of the Real Numbers Without Decimals
Posted: Dec 3, 2013 5:21 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Tuesday, December 3, 2013 9:09:53 AM UTC, WM wrote:

> This is the starting point of Cantor's first proof and all its variants: Let a sequence be gicen. With this assumption the limit is given as a defined number. To waste all naturals for the enumeration of the terms of the sequence is a very simple trick. Not convincing. |N could even be wasted for half of the terms. Or, after one sequence has been enumerated, the existence of further sequences could be used as a "proof" of uncountable sets.

Shouldn't really replying at all? I posted because it looked like you didn't understand what a "proof by contradiction" is. But then it seems you really don't understand what "proof by contradicting" is. "Zeit Geist"s fine post proved that the real numbers are uncountable by starting with an assumption that there is a sequence containing them all (which is _by definition_ the opposite of the reals being uncountable) and went on to demonstrate a contradiction, which means the assumption of the existence of such a sequence must be false.

You seem to object to the existence of such a sequence - not realising that this is _exactly_ the point. Except that I can't make any sense of your reasoning why you object, unlike Zeit Geist's original post which gives a very clear argument.


Date Subject Author
12/2/13
Read Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
William Elliot
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
G. A. Edgar
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
gnasher729
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/10/13
Read Re: Uncountability of the Real Numbers Without Decimals
Robin Chapman
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
Michael F. Stemper
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/6/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/6/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/6/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/6/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/6/13
Read Re: Uncountability of the Real Numbers Without Decimals
Brian Q. Hutchings
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
Brian Q. Hutchings
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
Brian Q. Hutchings
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
fom
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
albrecht
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
fom
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
ross.finlayson@gmail.com
12/8/13
Read Re: Uncountability of the Real Numbers Without Decimals
albrecht
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
fom
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
fom
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
fom
12/8/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/8/13
Read Re: Uncountability of the Real Numbers Without Decimals
albrecht
12/6/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/6/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
Michael F. Stemper
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
fom
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/2/13
Read Re: Uncountability of the Real Numbers
Virgil
12/3/13
Read Re: Uncountability of the Real Numbers
wolfgang.mueckenheim@hs-augsburg.de
12/3/13
Read Re: Uncountability of the Real Numbers
Virgil
12/5/13
Read Re: Uncountability of the Real Numbers
wolfgang.mueckenheim@hs-augsburg.de
12/5/13
Read Re: Uncountability of the Real Numbers
Virgil
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
gnasher729
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
gnasher729
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/3/13
Read Re: Uncountability of the Real Numbers
Virgil
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
gnasher729
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/7/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/8/13
Read Re: Uncountability of the Real Numbers Without Decimals
wolfgang.mueckenheim@hs-augsburg.de
12/8/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
Virgil
12/2/13
Read Re: Uncountability of the Real Numbers Without Decimals
ross.finlayson@gmail.com
12/4/13
Read Re: Uncountability of the Real Numbers Without Decimals
ross.finlayson@gmail.com
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
albrecht
12/3/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
albrecht
12/5/13
Read Re: Uncountability of the Real Numbers Without Decimals
Tucsondrew@me.com

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.