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The Smallest Number

Updated: Mar 7, 2022

I remember the day when one of my teachers, Anand Kumar, explained to us that there is no such thing as the smallest number. For any x that you propose as the smallest number, you can fit x/2, x/3, x/4, x/n and so on. In fact, you can fit infinite numbers between 0 and proposedly the smallest number x. There lie infinite numbers between any two points on the number line.

The smallest number must be limit x where x tends to 0 or dx. Does it exist? Absolutely. If you want to draw a number line, you would have to move the dimensionless tip of your pen by at least dx so you get 0 + dx. Without that infinitesimal movement, you will say forever at 0.

But the number line is imaginary. Why does it matter? It matters because what we call matter is perceived to have length, breadth, and depth. The three dimensions have magnitude. For magnitude (or for its illusion) to exist, there has to be the smallest magnitude. For any length l, there has to be dl. Without dl, you can’t go to any length from 0. Apparently, at the core of all physicality is an ideological entity. Without ideological entities, physicality seems impossible. Perhaps, Plato was right. Perhaps, not.

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