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real_logarithm [2016/02/10 14:56] nikolaj |
real_logarithm [2016/02/10 14:59] nikolaj |
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| Consider | Consider | ||
| - | $\log_r(r^n/r^k) = \log_r(r^{n-k}) = n-k = \log_r(r^n) - \log_r(r^k)$ | + | $\log_r(r^n/r^1) = \log_r(r^{n-1}) = n - 1 = \log_r(r^n) - \log_r(r^1)$ |
| - | 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 === | ||
