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real_logarithm [2016/02/10 14:57]
nikolaj
real_logarithm [2016/02/10 14:59] (current)
nikolaj
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 $\log_r(r^n/​r^1) = \log_r(r^{n-1}) = n - 1 = \log_r(r^n) - \log_r(r^1)$ $\log_r(r^n/​r^1) = \log_r(r^{n-1}) = n - 1 = \log_r(r^n) - \log_r(r^1)$
  
-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 ===
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