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Question Number 122053 by 676597498 last updated on 13/Nov/20

$$\mathrm{x}+\frac{1}{2}-\mathrm{E}(\mathrm{x}+\frac{1}{2})=?$$$$\mathrm{E}\left(\mathrm{x}\right)\mathrm{is}\mathrm{the}\mathrm{greatest}\mathrm{common}$$$$\mathrm{interger}\mathrm{of}\mathrm{x}$$

Commented by mr W last updated on 13/Nov/20

$$x-\left[x\right]=\left\{x\right\}$$$$\Rightarrow \mathrm{x}+\frac{1}{2}-\mathrm{E}(\mathrm{x}+\frac{1}{2})=\{x+\frac{1}{2}\}$$

Commented by 676597498 last updated on 13/Nov/20

$$\mathrm{thanks}$$$$\mathrm{wat}\mathrm{does}\left\{\mathrm{x}\right\}\mathrm{mean}$$

Commented by mr W last updated on 13/Nov/20

$$thefractionalpartofx:$$$$\left\{x\right\}=x-\left[x\right]$$

Answered by mathmax by abdo last updated on 15/Nov/20

$$\mathrm{x}+\frac{1}{2}-[\mathrm{x}+\frac{1}{2}]=\{\mathrm{x}+\frac{1}{2}\}(\mathrm{u}-\left[\mathrm{u}\right]=\left\{\mathrm{u}\right\})$$

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