Alef is Infinite

Infinity, the never ending. One of the most interesting ideas the human mind can conceive. Something that goes on and on and on and never stops. Imagine, for an instant, that this text contains infinitely many words. If you could read any number of words per second, still you would never finish it. This is more absurd than it sounds.

For example, the Pacific Ocean has so much less water than infinite water. The comparison is as good as comparing $1$ to infinity. The amount in the Pacific Ocean is not closer to infinity than a droplet. In order to convince yourself of this fact, think about spliting the Ocean in droplets and numbering them from droplet $1$ to droplet one gazillion or whatever. Still, the last one would be a finite number. Now think about what it means when we find the difference between two quantities: $10-4 = 6$ because $6$ is what you add to $4$ in order to get $10$. Very well. Now let us analyze whether or not droplet $2$ is closer to inifinity than droplet $1$: the number of droplets you would have to count to reach infinity from droplet $1$ is, well, infinitely many. If you literaly spent forever counting $1$ droplet per second, then you woud be able to finish. Same thing if you start from droplet $2$, $3$, $1000000$ or from any finite number for that matter.

If we use the symbol $\infty$ to represent infinity for now, we can convey what we said above in math notation the following way: $\infty - n = \infty,$ for any finite $n$. But there is a problem: is $\infty$ really a number in the sense of us being able to do arithmetic with it? Or is it simply a symbol representing the idea of never ending and, in that sense, not a number, so no arithmetic? Well, both.