Mathematics: (discrete math) see the picture in the attachment. how do i get started with this problem?

(discrete math) see the picture in the attachment.

Ответ:

adanamador8807

01.01.2022

Recall the definition of the floor function: if

is an integer and $n\le x$ , then $\lfloor x\rfloor=n$ . So $\lfloor4x\rfloor=n$ iff $\dfrac n4\le x$ .

So let's consider four case.

First, suppose $n\le x$ where $n\in\mathbb Z$ . It follows that

$\lfloor x\rfloor=\left\lfloor x+\dfrac14\right\rfloor=\left\lfloor x+\dfrac12\right\rfloor=\left\lfloor x+\dfrac34\right\rfloor=n$

because at most, we have

$n\le x$

Meanwhile, $\lfloor4x\rfloor=4n$ , which follows immediately from

$n\le x$

and so

$\lfloor4x\rfloor=4n=n+n+n+n=\lfloor x\rfloor+\left\lfloor x+\dfrac14\right\rfloor+\left\lfloor x+\dfrac12\right\rfloor+\left\lfloor x+\dfrac34\right\rfloor$

Then for the second case, you can consider what happens when you have $n+\dfrac14\le x$ ; for the third, $n+\dfrac12\le x$ ; and for the fourth, $n+\dfrac34\le x$ .

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Ответ:

simojo

11.05.2021

Mathematics

No, the above polynomials aren't similar as they don't have a constant scale factor

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(discrete math)
see the picture in the attachment.
how do i get started with this problem?

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