Actual Infinity in Reality?

[pocaracas]

What do you mean?

Don't you agree that 0.999999... actually is equal to 1? And not just potentially?

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

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

dude...
1/3 = 0.3333333....
2/3 = 0.6666666....
3/3 = 0.9999999.... = 1

[GrandizerII]

What do you mean?

Don't you agree that 0.999999... actually is equal to 1? And not just potentially?

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

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

---

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

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

dude...
1/3 = 0.3333333....
2/3 = 0.6666666....
3/3 = 0.9999999.... = 1

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

[SteveII]

This is getting silly--try to keep up. 

First, there is no "logic of actual infinity" for me to assail. There is no non-question-begging argument for it.

Ok, but you can still use a certain type of argument to disprove it. You get that, right? And in fact, that's what you have been trying to do anyway ... but you keep failing.

Well, some of that has to do with your attention or your comprehension (or both). I did make an argument--I even presented it formally. Here it is again (with a new line to be clearer). 

1. An actual infinite consists of real (not abstract) objects.
2. In 100% of our experiences and 100% of our scientific inquiries, quantities of real objects can have all the operations of addition, subtraction, multiplication and division applied to them. 
3. As Hilbert's Hotel shows, these operations cannot be applied to the concept of an actual infinite without creating contradictions and absurdities
4. Classical propositional logic does not allow for contradictory statements to be true. 
5. Therefore an actual infinite of real objects is logically impossible.

Infinite set theory is not a defeater for (2) because infinite set theory is not itself a conclusion derived from a logical process. To defeat (2) you have to give logical reasons why we should expect an infinite quantity of objects to behave fundamentally different than a finite quantity of objects. 

So, tell me where I "keep failing". 

Second, you can't answer Hilbert's Hotel without invoking set theory. I have not yet been supplied a reason why we have to invoke a mathematical assumption used only in mathematics to discuss rooms and guests. We wouldn't if there were 100, 1000 or even 10^10 rooms/guests. Poly has tried that tack that set theory is necessary for basic math operations. This is utterly ridiculous and I will point that out shortly.

Every grouping of stuff that can be mathematically represented as a set.

Sure if you have a mathematical purpose to do so. We don't. 

I see you have dropped your infinite causes is possible because there are no causes argument--good for you! It was a lousy argument.

I didn't drop it. You just didn't respond to the argument last time I referred to it. Plus, you seem to have forgotten Sean Carroll's causality is derived, not fundamental, quote. You do know that's what physicists believe, right?

And I believe that even your compadre Poly corrected you in thinking there is nothing to count back into infinity and therefore trigger the problem of traversing an actual infinite. I thought you dropped the argument. My mistake. If you still think there is no problem, I can't help that.

[LadyForCamus]

Denying math is what we’re resorting to now?

[SteveII]

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

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

dude...
1/3 = 0.3333333....
2/3 = 0.6666666....
3/3 = 0.9999999.... = 1

dude, 

1/3 does NOT equal 0.3333333...
2/3 does NOT equal 0.6666666...
3/3 does NOT equal  0.9999999...

you are just staying the same thing. It is wrong for the same reason. There is an infinite amount of 3's, 6's and 9's to the right. So it will NEVER equal the fraction or the whole number.

[polymath257]

What do you mean?

Don't you agree that 0.999999... actually is equal to 1? And not just potentially?

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

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

Um, sorry, but it is an actually true statement. The two sides are precisely equal. In every world.

OK, you have just shown your basic ignorance of math (as if you hadn't before).

---

dude...
1/3 = 0.3333333....
2/3 = 0.6666666....
3/3 = 0.9999999.... = 1

dude, 

1/3 does NOT equal 0.3333333...
2/3 does NOT equal 0.6666666...
3/3 does NOT equal  0.9999999...

you are just staying the same thing. It is wrong for the same reason. There is an infinite amount of 3's, 6's and 9's to the right. So it will NEVER equal the fraction or the whole number.

No, each and every one of those statements is precisely true *if* you understand the meaning of the notation. Clearly you do not.

All I can say is that you have clearly removed yourself from the realm of rationality. If you cannot accept *basic* mathematics, and thereby basic *logic*, we are done.

[SteveII]

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

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

dude...
1/3 = 0.3333333....
2/3 = 0.6666666....
3/3 = 0.9999999.... = 1

dude, 

1/3 does NOT equal 0.3333333...
2/3 does NOT equal 0.6666666...
3/3 does NOT equal  0.9999999...

you are just staying the same thing. It is wrong for the same reason. There is an infinite amount of 3's, 6's and 9's to the right. So it will NEVER equal the fraction or the whole number. An artifact of a base-10 number system.

[polymath257]

dude...
1/3 = 0.3333333....
2/3 = 0.6666666....
3/3 = 0.9999999.... = 1

dude, 

1/3 does NOT equal 0.3333333...
2/3 does NOT equal 0.6666666...
3/3 does NOT equal  0.9999999...

you are just staying the same thing. It is wrong for the same reason. There is an infinite amount of 3's, 6's and 9's to the right. So it will NEVER equal the fraction or the whole number. An artifact of a base-10 number system.

Yes, the requirement for an infinite expansion is a relic of base 10 in this case. In base 3, 1/3=.1 after all. But in base 3, 1/10 requires an infinite expansion. In both, the square root of 2 requires an infinite expansion. In all cases, the meaning of the infinite expansion gives the appropriate equality.

[SteveII]

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

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

Um, sorry, but it is an actually true statement. The two sides are precisely equal. In every world.

OK, you have just shown your basic ignorance of math (as if you hadn't before).

---

dude, 

1/3 does NOT equal 0.3333333...
2/3 does NOT equal 0.6666666...
3/3 does NOT equal  0.9999999...

you are just staying the same thing. It is wrong for the same reason. There is an infinite amount of 3's, 6's and 9's to the right. So it will NEVER equal the fraction or the whole number.

No, each and every one of those statements is precisely true *if* you understand the meaning of the notation. Clearly you do not.

All I can say is that you have clearly removed yourself from the realm of rationality. If you cannot accept *basic* mathematics, and thereby basic *logic*, we are done.

Nope. The fact that we assign 1 to 0.99999... is a convenience in mathematics. 

What you are really saying is 1 = 1 - 1/infinity. 

Since 1/infinity does not equal zero, then 1 does not equal 0.99999...

[polymath257]

Um, sorry, but it is an actually true statement. The two sides are precisely equal. In every world.

OK, you have just shown your basic ignorance of math (as if you hadn't before).

---

No, each and every one of those statements is precisely true *if* you understand the meaning of the notation. Clearly you do not.

All I can say is that you have clearly removed yourself from the realm of rationality. If you cannot accept *basic* mathematics, and thereby basic *logic*, we are done.

Nope. The fact that we assign 1 to 0.99999... is a convenience in mathematics. 

What you are really saying is 1 = 1 - 1/infinity. 

Since 1/infinity does not equal zero, then 1 does not equal 0.99999...

Nope that is NOT what the symbolism means. It is not just a convenience. Those are actual, exact, equalities.

I assure you, you don't want the technical definition. You wouldn't be able to handle the logic of the definition.