= Exponential Chebyshev system
{title2=$e^{\lambda_0x},\ldots,e^{\lambda_nx}$}
Exponentials with distinct real exponents form a <Chebyshev system> on every nondegenerate real interval. For an inductive proof, multiply a candidate combination by $e^{-\lambda_0x}$. If it has $n+1$ zeros, <Rolle's theorem> gives at least $n$ zeros of its derivative, a combination of the $n$ exponentials with exponents $\lambda_i-\lambda_0$, $i>0$. The inductive zero bound forces all those coefficients to vanish. The remaining constant also vanishes, a contradiction.
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