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Question Number 164623 by mathocean1 last updated on 19/Jan/22

$$Givena,b\in \mathbb{R}.$$$$Showthat:$$$$\left[a\right]+\left[b\right]⩽[a+b]⩽\left[a\right]+\left[b\right]+1$$

Answered by mahdipoor last updated on 19/Jan/22

$$\left[b\right]⩽b<\left[b\right]+1\Rightarrow a+\left[b\right]⩽a+b<a+\left[b\right]+1\Rightarrow$$$$[a+\left[b\right]]⩽[a+b]⩽[a+\left[b\right]+1]\Rightarrow$$$$\left[a\right]+\left[b\right]⩽[a+b]⩽\left[a\right]+\left[b\right]+1$$

Commented by mathocean1 last updated on 19/Jan/22

$$thanks$$

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