Actual Infinity in Reality?

[polymath257]

OK, then what do *you* call it when something doesn't correspond in quantity to a counting number?

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A point represents a location between 0 and 1. Wasn't that obvious?

And yes, there is an infinite number of such points.

And yes, we *do* reach the end. The *logic* that I presented shows that. Your *claim* is based on a faulty *assumption* that you cannot a complete an infinity. And no, that is NOT a fact. Remember, to be infinite *only* means that it cannot be put into correspondence with some counting number. it does NOT mean 'has no bound'. it does NOT mean 'goes on forever'. it does NOT mean 'has no end'. The example of the sequence we have been considering shows the differences.

So are you saying that counting numbers have an end?   Or that only non-counting numbers do not end?  It seems to me, that you are attempting to make a distinction without a difference.

Also just to clarify,  would you agree that these locations, do not necessarily correspond to anything physical on the line, or involved in the motion.  They serve a purpose, for an academic model but are not an actual infinite number of things?

The counting numbers do not 'end' if ordered in the usual way. But, for example, the *negative* counting numbers *do* have an 'end' when ordered int he usual way. The question of 'having an end' depends on the *order*, not on the quantity.

No, those locations correspond to points on the physical line. And yes, they are an *actual* infinity of points.