Let us consider the set $C[0,1]$ of all continuous functions. How to show that $\{f_{\alpha}:\alpha\ge 0\}$, where $ f_\alpha (x)=x^{ \alpha}$ for all x is linearly independent. In case of polynomials we can do it easily by equating with zero polynomials. How to show here? Please help.
2026-04-09 00:46:16.1775695576
Showing linear independence
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