Question

Define the statement$f(x,y)\text{is}\mathrm{\Omega }\left(g\right(x,y\left)\right)$

Short answer

The statement$f(x,y)\text{is}\mathrm{\Omega }\left(g\right(x,y\left)\right)$means that there exist constants such that$\left|f\right(x,y\left)\right|\ge C\left|g\right(x,y\left)\right|$ where$x>k_1$ and$y>k_2$

Step-by-step solution

Step 1:

We know that definition of big omega notation is:

Let two functions f and g from the set of integers or the set of real numbers to the set of real numbers. We say that $f(x,y)\text{is}\mathrm{\Omega }\left(g\right(x,y\left)\right)$ if there are positive constants C and k such that

$\left|f\right(x\left)\right|\ge C\left|g\right(x\left)\right|$whenever x > k

Step 2:

For the given question, adding one more variable$k_2$for y then,

The definition of statement$f(x,y)\text{is}\mathrm{\Omega }\left(g\right(x,y\left)\right)$means that there exist constantssuch that$\left|f\right(x,y\left)\right|\ge C\left|g\right(x,y\left)\right|$ whenever$x>k_1$ and$y>k_2$