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May 17th, 2018, 11:53 AM   #11
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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.
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May 17th, 2018, 12:38 PM   #12
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Oh oh, I better get out of here.
NOW you're making sense!
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May 18th, 2018, 08:26 AM   #13
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zylo, did you really mean to say "the reals are countable"?
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May 18th, 2018, 08:44 AM   #14
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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
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May 18th, 2018, 10:04 AM   #15
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Quote:
Originally Posted by zylo View Post
Yes

My latest proof s given here:
Real Numbers are a Subset of the Rationals
https://www.psychologytoday.com/us/b...rama-addiction
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May 18th, 2018, 10:55 AM   #16
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Originally Posted by zylo View Post
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.
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May 19th, 2018, 03:58 AM   #17
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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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