An algebra problem by sudoku subbu

Algebra Level 1

$\lfloor -2.3 \rfloor = \, ?$

-1 -2 -3 -4

1 solution

Pranjal Jain
Jan 18, 2015

[x] is the greatest integer less than OR equal to x.

Neglect $-2$ and $-1$ as they are neither less nor equal to $-2.3$

Out of $-3$ and $-4$ , $-3$ is greater, so $[-2.3]=-3$

here [....] means greatest integer function

sudoku subbu - 6 years, 4 months ago

That's what I have written! I just mentioned definition of Greatest Integer Function!

Pranjal Jain - 6 years, 4 months ago

its ok meet you next time

sudoku subbu - 6 years, 4 months ago

We can also use the formal definition, albeit it means the same as your explanation,

$\left\lfloor x \right\rfloor=\sup(\{y\mid y\leq x~,~y\in \mathbb{Z}\})$

where $\sup (A)$ denotes the supremum of the set $A$ .

For $x=(-2.3)$ , we have,

$\left\lfloor (-2.3) \right\rfloor=\sup(\{y\mid y\leq (-2.3)~,~y\in \mathbb{Z}\})\\ \implies \left\lfloor (-2.3)\right\rfloor=\sup(\{y\mid y\in (-\infty,-3]~,~y\in \mathbb{Z}\})=(-3)$

Prasun Biswas - 6 years, 3 months ago

An algebra problem by sudoku subbu

1 solution

0 pending reports