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 real_logarithm [2016/02/10 14:57]nikolaj real_logarithm [2016/02/10 14:59] (current)nikolaj Both sides previous revision Previous revision 2016/02/10 14:59 nikolaj 2016/02/10 14:57 nikolaj 2016/02/10 14:56 nikolaj 2016/02/10 14:55 nikolaj 2016/02/10 14:55 nikolaj 2016/02/10 11:37 nikolaj 2016/02/10 11:37 nikolaj 2016/02/10 11:36 nikolaj 2016/02/10 11:33 nikolaj 2015/04/15 14:06 nikolaj 2014/03/21 11:11 external edit2014/02/25 21:19 nikolaj 2014/02/25 21:19 nikolaj 2014/02/25 21:19 nikolaj 2014/02/13 16:13 external edit2013/09/08 15:25 nikolaj 2013/09/08 15:22 nikolaj 2013/09/08 15:22 nikolaj 2013/09/07 20:19 nikolaj 2013/09/07 20:19 nikolaj 2013/09/07 20:18 nikolaj 2013/09/07 20:18 nikolaj 2013/09/07 20:11 nikolaj created 2016/02/10 14:59 nikolaj 2016/02/10 14:57 nikolaj 2016/02/10 14:56 nikolaj 2016/02/10 14:55 nikolaj 2016/02/10 14:55 nikolaj 2016/02/10 11:37 nikolaj 2016/02/10 11:37 nikolaj 2016/02/10 11:36 nikolaj 2016/02/10 11:33 nikolaj 2015/04/15 14:06 nikolaj 2014/03/21 11:11 external edit2014/02/25 21:19 nikolaj 2014/02/25 21:19 nikolaj 2014/02/25 21:19 nikolaj 2014/02/13 16:13 external edit2013/09/08 15:25 nikolaj 2013/09/08 15:22 nikolaj 2013/09/08 15:22 nikolaj 2013/09/07 20:19 nikolaj 2013/09/07 20:19 nikolaj 2013/09/07 20:18 nikolaj 2013/09/07 20:18 nikolaj 2013/09/07 20:11 nikolaj created Line 14: Line 14: $\log_r(r^n/​r^1) = \log_r(r^{n-1}) = n - 1 = \log_r(r^n) - \log_r(r^1)$ $\log_r(r^n/​r^1) = \log_r(r^{n-1}) = n - 1 = \log_r(r^n) - \log_r(r^1)$ - vs. + vs. ${\mathrm {dim}}({\mathbb R}^n/​{\mathbb R}^1) = {\mathrm {dim}}({\mathbb R}^{n-1}) = n - 1 = {\mathrm {dim}}({\mathbb R}^n)-{\mathrm {dim}}({\mathbb R}^1)$ ${\mathrm {dim}}({\mathbb R}^n/​{\mathbb R}^1) = {\mathrm {dim}}({\mathbb R}^{n-1}) = n - 1 = {\mathrm {dim}}({\mathbb R}^n)-{\mathrm {dim}}({\mathbb R}^1)$ + + where by ${\mathbb R}^n/​{\mathbb R}^1$ we mean a quotient vector space . === Theorems === === Theorems ===