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I want to prove that $e^x\ge 1+x$ for each $x\in\mathbb{R}$.

I can't use neither derivative nor logs.

Edit: I SAID I can't use derivatives... and Taylor's theorem use this...

user74411
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    It would be interesseting to know what you can use, that is: How do you define $\exp$? – martini Jun 14 '13 at 06:13
  • Maybe it couold follow from this definition of an exponential function: $e^{x}=\lim_{x\to\infty}(1+\frac{x}{n})^{n}$ – Mykolas Jun 14 '13 at 20:41
  • @Mykolas Indeed, that definition and Bernoulli's inequality are enough. –  Jul 21 '15 at 23:09

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