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: Teaching moronic trolls like JG about their own flawed theories
Replies: 5   Last Post: Oct 4, 2017 6:48 AM

Advanced Search

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

Posts: 1,716
Registered: 1/23/16
Re: Teaching mainstream morons about their own flawed theories:
Every Cauchy sequence of real numbers converges to a limit.

Posted: Sep 27, 2017 6:49 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Wednesday, September 27, 2017 at 3:53:39 PM UTC+2, John Gabriel wrote:

> "Every Cauchy sequence of real numbers converges to a limit."

Yes, idiot. In the context of the reals, that is. *sigh*

Man, these lectures are dealing with real analysis.

> In spite of this, you will get thousands of [reasonable people,
> knowing their stuff] (Klyver and "Me" and Burse included) talking
> about Q as if it is not part of R.

The reason for this is that if we "build up" the number systems, staring just with IN (i.e. the Peano axioms) there's indeed a set Q which (at that point) is NOT "Part of IR, especially since at that point IR has not yet be defined.


> For example [...] Klyver will harp on the [...] fact that a Cauchy sequence
> of rationals may not converge to a rational number

Right, that's exacty the relevant point.

> [and] this [just] mean[s] the sequence does not converge the context of the rational numbers. Right!

> ... if every Cauchy sequence converges to some *LIMIT* ...

In the context of the rational numbers it's NOT the case that every Cauchy sequence converges to some *LIMIT*.

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.