Ideas in the Night

Tag Archives: set theory

Set Z consists of all negative and positive integers and zero:

Z = {…, -3, -2, -1, 0, 1, 2, 3, …}.

Human’s intuition easily make to think that zero (0) is the middle point of set Z. But is it?

In every finite subset of set of Z {-p, -p + 1, –p + 2, …, 0, …, p – 2 , p – 1, p} (p > 3) zero is the middle point on grounds of symmetry:

|(-p) – 0| = |p – 0| = p

(With difference in absolute values, one gets the distance between points.)

But what about the whole set Z? It is an infinite set without beginning or end. Can it have a middle point?

I’ll take a role of a creator. I say: I create the set Z from zero to negative and positive infinity. Someone says: Then zero is the middle point. I answer: No, I ”started” the creation from zero, but after creation of my infinite work, my work doesn’t have a start or an end. Therefore it does not have a middle point.

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Image courtesy of Sira Anamwong at FreeDigitalPhotos.net

Back to the role of a blogger: Because the set Z doesn’t have a start or an end, it doesn’t have a middle point. One can’t measure the distance from “infinity to finite number zero”, at least we humans can’t. The best we can say is that the distance in this case is infinite, but that’s all.

One could also ask: Does set N have a middle point? (consists of all positive integers and is an infinite set) In this case human’s intuition doesn’t make it to think that set would have a middle point.

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