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Question Number 145273 by ArielVyny last updated on 03/Jul/21

$$showthat\mathrm{\forall }x\in \mathbb{R}x-1⩽E\left(x\right)⩽x$$

Answered by mathmax by abdo last updated on 04/Jul/21

$$\mathrm{we}\mathrm{have}\left[\mathrm{x}\right]⩽\mathrm{x}<\left[\mathrm{x}\right]+1\Rightarrow \left[\mathrm{x}\right]⩽\mathrm{x}\mathrm{and}\mathrm{x}-1<\left[\mathrm{x}\right]\Rightarrow$$$$\mathrm{x}-1<\left[\mathrm{x}\right]⩽\mathrm{x}$$

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