Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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


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

Topic: 1.17 - Is it sensible to link cardinality of two sets with a bijection?
Replies: 7   Last Post: Jun 7, 2014 3:46 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
thenewcalculus@gmail.com

Posts: 1,616
Registered: 11/1/13
1.17 - Is it sensible to link cardinality of two sets with a bijection?
Posted: Jun 6, 2014 4:42 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

A small investigation of the following applet, will reveal that this is an absurd idea:

https://www.filesanywhere.com/fs/v.aspx?v=8b6d658f5c637279b297

The intervals (0,1) and (0.5, 0.75) are mapped using the bijective function RtoI() and its inverse ItoR().

Never mind that the finite line segments are of lengths 1 and 0.25 respectively, but idiot Cantorites imagine in their dysfunctional minds, that these two intervals have the same number of elements, that is, numbers.

However, the problem is that not every output of the bijection is a rational number! In most cases, it is an incommensurable magnitude.

So one has:

numbers to numbers
numbers to incommensurable magnitudes
incommensurable magnitudes to numbers
incommensurable magnitudes to incommensurable magnitudes

Each set consists of two types of elements: numbers and incommensurable magnitudes. This is in total violation of the definition of set, which states that elements must be distinct and of the same type. While numbers exist as distinct elements, incommensurable magnitudes DO NOT exist as distinct elements.

For example, what is pi or sqrt(2)? The whole idea of bijection implying same cardinality is therefore absurd!

Comments are not welcome. This comment is produced in the interests of public education.



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

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.