Infinitely Finite (slicing infinitely)

If an apple was divided continuously uncountably, divided continuously to infinity, then it’s infinite division of finite apple. Is it possible? No.

• But the fact support it. Through observations, it only involves one apple. And splitting one apple infinitely, does not become as many as two apples. Still we are dealing with the same (one) apple.

Where is the discrepancy of the observation? It’s because we use the experiment not so deeply clear. We need closer enough the object that we imagine. We zoom in so closely, then we will see the lack of carefulness of our previous observations.

When ice splits indefinitely, the distance from the left side of ice to the right side of ice will increase indefinitely which has the following consequences:

1. the amount of ice before / after splitting remains the same, while the area of ​​water (which holds ice) shrinks, then it is not an infinite division, but rather the shrinking of water, converting to ice, so that there is no limitless division.
2. the amount of ice before / after splitting remains the same, while the area of ​​water (which contains ice) increases, then this violates the axioma (the total amount of ice + water exceeds itself)

But for some of us, such imaginative observations are still felt blurry, unclear. Let’s try to go down further, even deeper. We try to dig down with the axiom so deeply to see that the axiom is still alive to argue "infinite in limitation".

In the simulation of gedanken experiment here we need to try various scenarios like a laboratory, to confirm clear observation.

We use parable with an apple, wrapped so tightly inside thin aluminum, that no cavity is found in between the apple and the inner side of aluminum layer that encloses an apple.

Now we simulate the division to an apple by itself, is it possible?

1. No: because the apple is tightly wrapped, so there is no cavity / space that separates the apple.
2. Yes, you can: this means that the wrapper will tear, because each division will leave space between an apple. From this, it is clear that infinite division involves an expansion from the original size (calculated from the most left side of the apple to the most right side of the apple). So? It is impossible for infinite as part of division finite.

The failure of previous observations on the division of apples is that the process of logical imagination is not really realistic. Not completely furnished, it still involves division mathematically but not fully imaginary.

Correcting our viewpoint:

• if the amount of ice before / after splitting remains the same, then the area of ​​water (which contains ice) must expand (compensate) to make room for separation between chunks of ice, so this violates axiom, where the total amount of ice + water exceeds itself which is a violation of axiom.

Conclusion: Infinite does not exist in limitation.