Actual Infinity in Reality?

[RoadRunner79]

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Why does this not work when you do the same process that you used to show an infinity, and is also the one in Zeno’s paradox?  You always go to something different and don’t address this in the dichotomy paradox.

Note for everyone else. You may notice, that the math in Zeno’s paradox will never reach it’s goal. If the math gives you trouble, you can see that this same process is being used to show that there is an infinite amount of numbers, that you cannot get to the destination, then you add another infinite, and can then reach the destination. In more ways than one... what is being claimed simply does not add up.

OK, again, part of the problem is the definition of the term 'infinity'. You claim an infinity cannot have an end and that it cannot be bounded. That is simply false. The sequence of 9's above is a wonderful example.

For each one in the sequence, there are an infinite number that are larger. This is true. So it is an infinite collection (whether potential or actual is irrelevant here).

It is also bounded since everything in that sequence is less than 1. Each and every term of that sequence is smaller than 1.

So, we have an infinity that is bounded.

The resolution is easy: we have two different notions of boundedness here. One has to do with where in the e a term is and the other has to do with where in the interval from 0 to 1 that term is. The sequence is unbounded in the first sense and bounded in the second. But they are two different notions of being bounded, so there is no contradiction there.

When you ask if we can 'get through' a sequence, you have to specify exactly what you mean. Strictly speaking there isn't even a process here. There are two collections: the terms of the sequence and the numbers between 0 and 1. Both are infinite. You don't get to 1 by staying in the sequence. But that isn't relevant if you want to get to one from within the numbers between 0 and 1.

But we *do* get to the destination, which means we *do* go through all those points. If you deny that, exactly which point do we not go through? At which point does the division break down?

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You seem to get distracted easily and go off on tangents, so lets keep this simple.
Let's look to Zeno's paradox and systematically work through this. Do you agree or disagree with the following.

The dichotomy paradox (or runners paradox) demonstrates an infinite quantity of numbers between any two points, if one is able to cut in half the distance from current location, and the end.  One can continue in this process ad infinitum with the half as the current point and a new halfway point and always have a new number.  I believe you will agree here, you in fact used this (or something very similar) to show that there is an infinity of real numbers between any two numbers.  Do you agree?

According to the above, in traveling between two points, you will always have another half way point to overtake, prior to reaching the destination point.  That is you will always have another number between your current location and end.  Do you agree?

You can likewise reverse this process and work towards the beginning of the journey.  You will end up with a similar outcome where you can always have another halfway point, between the start and the current halfway point.

Would you agree with these statements in Zeno's paradox?

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That's ridiculous. 0.99999... will NEVER equal 1. Not even potentially

In no world does that make any sense to assert that.

You're objectively wrong.

It's the same fucking number written differently.

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Poor Steve, and just to spoonfeed/confuse him a little more:

1/3 * 3 = 1
0.333333... * 3 = 0.999999...

1/3 = 0.333333...

1/3 * 3 = 0.333333... * 3 = 1

1/3 * 3 = 0.999999... = 1

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And to put it logically.... there is no possible space between 0.999999... and 1 to make it a separate number. It's no more or less than 1, ergo it's 1.

On an integer line, there is no possible space between 1 and 2,  or for that matter 2 and 3 to make a separate number.   Are these equal as well?