I'm trying to say that as the number of random coordinate points points you plot approaches infinity, it is equivalent to an area integral where each point is an infinitesimally small $\mathrm{d}x \times \mathrm{d}y$ over the same interval.

The current expression I have is: $$\lim\limits_{n\rightarrow\infty} Pr[0 \leqslant RND(X_{n}) \leqslant 1, -1 \leqslant RND(Y_{n}) \leqslant 1] = \int\limits_{y=-1}^{1}~\int\limits_{x=0}^{1}\,\mathrm{d}x \mathrm{d}y$$

How could this be improved?



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