MHB Proof of Equality for Odd Integers with Floor Function

[tmt1]

I need to prove or disprove that

$$ \left\lfloor{\frac{n}{2}}\right\rfloor= \left\lfloor{ \frac{n - 1}{ 2}}\right\rfloor$$ where n is an odd integer.I start with something like,

$$\left\lfloor{\frac{2k + 1}{2}}\right\rfloor$$

and then

$$\left\lfloor{k + \frac{1}{2}}\right\rfloor$$ which equals $$k$$

But

$$ k = \frac{n - 1}{2}$$

So is that enough proof for the question? or is it wrong?

 

[kaliprasad]

I need to prove or disprove that

$$ \left\lfloor{\frac{n}{2}}\right\rfloor= \left\lfloor{ \frac{n - 1}{ 2}}\right\rfloor$$ where n is an odd integer.I start with something like,

$$\left\lfloor{\frac{2k + 1}{2}}\right\rfloor$$

and then

$$\left\lfloor{k + \frac{1}{2}}\right\rfloor$$ which equals $$k$$

But

$$ k = \frac{n - 1}{2}$$

So is that enough proof for the question? or is it wrong?

as n is odd a and n = 2k+1 so $ k = \frac{n - 1}{2}$ so it should be sufficient