i don't buy it. the snakes are occupying R2, they aren't members of it. no snake is a pair of the form (x,y) for x and y in R; rather, the snakes on the plane are situated at such points (or occupy collections of such points). points are in R2 - other two-dimensional objects occupying the plane (lines, curves, polygons, et c.) do not stand in the set-theoretic membership relationship to R2.
η: for that matter, i have a B.A. in math, and most of the time i remember set-membership being pronounced ‘in’. it's likely that this is because i focused on logic and algebra - ‘on’ is probably more common in some other areas.
Yep. See my comment to "lostmyreligion" above for a *little* more explanation. :)
BTW I enjoy reading how you're doing in Math. It's interesting to see it from the other side of the table for me. I'm glad to see you're doing well in it. :)
I'm actually doing metric conversion crap right now. I'm not sure if it's the book or if my brain has just changed, but I am getting this stuff way more than I did in the past. This is all really basic though, anything more advanced still boggles me.
(Quibble: although I never took topology or differential geometry, I have a strong suspicion that there are things that are isomorphic--even diffeomorphic--to ℜ2 that aren't planes. :) )
Anyway, clearly the real question is whether snakes can tile the plane. ;)
no subject
Date: 2008-03-15 01:10 am (UTC)no subject
Date: 2008-03-15 01:22 am (UTC)no subject
Date: 2008-03-15 01:41 am (UTC)R2 makes that two-dimensional.
The "E" means "member of the set", but is sometimes abbreviated by saying "on" instead.
You can figure it out from there.
no subject
Date: 2008-03-15 01:46 am (UTC)η: for that matter, i have a B.A. in math, and most of the time i remember set-membership being pronounced ‘in’. it's likely that this is because i focused on logic and algebra - ‘on’ is probably more common in some other areas.
no subject
Date: 2008-03-15 01:48 am (UTC)no subject
Date: 2008-03-15 02:23 pm (UTC)*sigh* Just when I had finally blocked all my memories of college math, too! ;) (my major)
no subject
Date: 2008-03-15 01:42 am (UTC)no subject
Date: 2008-03-15 01:43 am (UTC)no subject
Date: 2008-03-15 01:44 am (UTC)no subject
Date: 2008-03-15 01:46 am (UTC)BTW I enjoy reading how you're doing in Math. It's interesting to see it from the other side of the table for me. I'm glad to see you're doing well in it. :)
no subject
Date: 2008-03-15 02:39 am (UTC)no subject
Date: 2008-03-15 06:09 am (UTC)(Quibble: although I never took topology or differential geometry, I have a strong suspicion that there are things that are isomorphic--even diffeomorphic--to ℜ2 that aren't planes. :) )
Anyway, clearly the real question is whether snakes can tile the plane. ;)
no subject
Date: 2008-03-15 08:41 pm (UTC)no subject
Date: 2008-03-16 12:23 am (UTC)no subject
Date: 2008-03-17 04:06 am (UTC)