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 May 17th, 2018, 10:53 AM #11 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,364 Thanks: 100 The rationals are just another one dimensional vector field with an infinite number of vectors, which can be put into 1:1 correspondence with the reals, as I have shown (the reals are countable) By finite I mean having a max number. 1,2,3,4,........... is not finite 1,2,3 is. Oh oh, I better get out of here.
May 17th, 2018, 11:38 AM   #12
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Quote:
 Originally Posted by zylo Oh oh, I better get out of here.
NOW you're making sense!

 May 18th, 2018, 07:26 AM #13 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,192 Thanks: 871 zylo, did you really mean to say "the reals are countable"?
May 18th, 2018, 07:44 AM   #14
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Quote:
 Originally Posted by Country Boy zylo, did you really mean to say "the reals are countable"?
Yes

My latest proof s given here:
Real Numbers are a Subset of the Rationals

May 18th, 2018, 09:04 AM   #15
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Quote:
 Originally Posted by zylo Yes My latest proof s given here: Real Numbers are a Subset of the Rationals

May 18th, 2018, 09:55 AM   #16
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Quote:
 Originally Posted by zylo The rationals are just another one dimensional vector field with an infinite number of vectors...
Be careful with what you say: the rationals are a field, and they are a vector space over themselves. But they are not a "vector field".

Note that there's more to a vector space $V$ than just the set $V$; there's also the field of scalars $F$.

For example, if $V = \mathbb{R}$ and $F = \mathbb{R}$, then $V$ is a 1-dimensional vector space.

However, if $V = \mathbb{R}$ and $F = \mathbb{Q}$, then $V$ is an infinite dimensional vector space.

Your drivel about $\mathbb{R}$ being countable doesn't even dignify a response.

May 19th, 2018, 02:58 AM   #17
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Quote:
 Originally Posted by zylo Yes My latest proof s given here: Real Numbers are a Subset of the Rationals
That's a very old "proof" that is well known to be fallacious. Errors are pointed out in the responses to that post.

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