| Line 1: | Line 1: | ||
<math>(\Rightarrow)</math> | <math>(\Rightarrow)</math> | ||
If there is a sequence of odd polynomials <math> {p_n(x)} </math> with <math>p_n \rightarrow f </math>, then <math> f(0) = 0 </math>. | If there is a sequence of odd polynomials <math> {p_n(x)} </math> with <math>p_n \rightarrow f </math>, then <math> f(0) = 0 </math>. | ||
| − | Since <math>p_n(x)</math> are odd polynomials, then <math> p_n(0) = 0. </math>. Then <math>f(0) = \lim_{n \rightarrow \ | + | Since <math>p_n(x)</math> are odd polynomials, then <math> p_n(0) = 0. </math>. Then <math>f(0) = \lim_{n \rightarrow \infty} p_n(0) = 0</math> |
Revision as of 01:17, 10 July 2008
$ (\Rightarrow) $ If there is a sequence of odd polynomials $ {p_n(x)} $ with $ p_n \rightarrow f $, then $ f(0) = 0 $. Since $ p_n(x) $ are odd polynomials, then $ p_n(0) = 0. $. Then $ f(0) = \lim_{n \rightarrow \infty} p_n(0) = 0 $
