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## What if 0 is just a concept with no actual real-world counterpart?

Have you ever noticed that when you get 0 involved in even the simplest multiplicative operations, it manages to screw them up? For instance, take the functions f(x)=1/x and g(x)=xx. As for f(x)=1/x, f(0)=1/0, an expression that, from one side of the equation's graph, appears to represent positive infinity, but from the other side appears to represent negative infinity. And what about g(x)=xx? That seems to be a pretty straightforward operation. Yet, g(0)=00; conventionally x0=x/x, but 0/0's value is context-dependent, and no context was set by use of g(0); hence, g(0) could mean anything depending on its own context, but by using it in two different contexts, we could get, say, g(0)=2 and g(0)=3, and since 2$$\neq$$3, one could conclude by substitution that 0/0$$\neq$$0/0. But what about just using 2 or just using 3? 2=2 and 3=3, so substituting from either of these cases, we could find that 0/0=0/0. So there you have it: an expression that looks like two completely different terms depending on what side you approach it from and an expression that both does and does not equal itself. Weird, right? Why is it that all the operations in math that are illegal, that have no answer at all, all seem to trace back somehow to li'l ol' harmless 0? If so many things related to 0 are illegal operations, might it then be possible that in mathematics that run completely parallel to the functioning of the universe, 0 itself should not exist? Back when 0 was first invented, I'm certain it was during the early years of mathematics, where it had much more to do with the real world, back when it was used for tallying; 0 was probably used to represent, for example, the complete absence of oxen to pull carts, or chickens to lay eggs, or maybe just bananas. But is there ever a complete absence of bananas? Isn't it possible that no matter how many bananas you take away, there's always just a little tiny bit of banana left over? You can't really get rid of bananas completely; they're dropping atoms and molecules all over the place with each step you take while carrying them. Parts of themselves. Fractions of bananas. Maybe even if you try to take away parts of those atoms and molecules, there will always be little bits of them left. Maybe everything trails infinitesimal pieces of itself wherever it goes. Why does there have to be a 0, a point where is absolutely nothing? What if there's never absolutely none of something? If that's the case, 0 shouldn't even exist, and if it does, it's a mathematical concept with no real-world parallel. Of course, all of this is hypothetical; if I knew any of this for sure, I wouldn't even be talking about it here.