ciphergoth comments on Bizarre Illusions - Less Wrong

11 Post author: MrHen 27 January 2010 06:25PM

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Comment author: Zack_M_Davis 08 February 2010 10:05:35AM 0 points [-]

I see that we could have a 'vector space' of infinite-dimensional vectors where each vector (a1, a2, ..., an, ...) represents a number N where N = (P1^a1)(P2^a2)...(Pn^an)... and Pi are the ordered primes.

Oh! And orthogonal vectors are relatively prime!

Comment author: ciphergoth 08 February 2010 11:15:17AM 1 point [-]

I'm not sure that the idea of orthogonality is defined for modules, is it? Is there a standard definition of an inner product for a Z-module?

Comment author: komponisto 08 February 2010 06:49:48PM 1 point [-]

I'm not sure that the idea of orthogonality is defined for modules, is it? Is there a standard definition of an inner product for a Z-module?

Yes; the same definition works. See here.

Comment author: Zack_M_Davis 09 February 2010 12:05:14AM 0 points [-]

Yay! I actually got something right!

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