The meaning of infinity

[Jokodo]

0.999... = 0.111... * 9, obviously.

In the meantime, are you or are you not claiming that 9/9 != 1?

 

[untermensche]

0.999... = 0.111... * 9, obviously.

In the meantime, are you or are you not claiming that 9/9 != 1?

Never came close to saying it.

I have said that 0.999.... never becomes 1. It is a string of 9's forever in that notation.

That is what I have said.

Change the notation or perform some operations to it and it might become something else.

 

[Jokodo]

0.999... = 0.111... * 9, obviously.

In the meantime, are you or are you not claiming that 9/9 != 1?

Never came close to saying it.

Oh yes, you did.

The fact that you don't understand this shows exactly how qualified you are to reinvent math.

And 0.999... doesn't become 1, it is one. It's a feature of the decimal notation that this specific number has two equivalent representation, in the same way it's a feature of the roman numerals that IIII and IV are equivalent.

 

[untermensche]

0.999... = 0.111... * 9, obviously.

In the meantime, are you or are you not claiming that 9/9 != 1?

Never came close to saying it.

Oh yes, you did.

The fact that you don't understand this shows exactly how qualified you are to reinvent math.

And 0.999... doesn't become 1, it is one. It's a feature of the decimal notation that this specific number has two equivalent representation, in the same way it's a feature of the roman numerals that IIII and IV are equivalent.

0.999... is not 1.000...

I am not reinventing anything.

If something is defined as an infinite string of 9's then that is what it is.

Some who see the emperors new clothes so well can try to tell me it somehow by magic becomes something else.

I do not believe their nonsense.

They have been brainwashed.

0.999... is infinitely close to 1.

There is nothing between 0.999... and 1

That is not the same thing.

But in the real world calling it 1 makes no difference.

There is no real world difference between 0.999... and 1.

You cannot have 0.999...% of an apple.

But there is a difference in conception.

 

[Jokodo]

Oh yes, you did.

The fact that you don't understand this shows exactly how qualified you are to reinvent math.

And 0.999... doesn't become 1, it is one. It's a feature of the decimal notation that this specific number has two equivalent representation, in the same way it's a feature of the roman numerals that IIII and IV are equivalent.

0.999... is not 1.000...

It is not in the same sense as IIII is not IV: They're different representations of the same entity.

I am not reinventing anything.

If something is defined as an infinite string of 9's then that is what it is.

An infinite string of nines is not a number, it's a (unrealisable, idealised) written representation of a number. A number that, in this case, happens to be identical to 1.0..., or 1.0, or 1

Some who see the emperors new clothes so well can try to tell me it somehow by magic becomes something else.

Nothing becomes something else by virtue of the fact that there are two ways to refer to the same entity. 180° East is the same imaginary line as 180° degrees West. 90° N, 20° East is the same point as 90° N, 132° West (both refer unambiguously to the North pole). Roman X is the same number as decimal 10, binary 1010 or hexagesimal A.

I do not believe their nonsense.

They have been brainwashed.

0.999... is infinitely close to 1.

There is nothing between 0.999... and 1

That is not the same thing.

But in the real world calling it 1 makes no difference.

There is no real world difference between 0.999... and 1.

You cannot have 0.999...% of an apple.

But there is a difference in conception.

There's neither a practical nor a conceptual difference. 0.999... = 9 * 0.111... = 9 * 1/9 = 9/9 = 1.

 

[untermensche]

It is not in the same sense as IIII is not IV: They're different representations of the same entity.

Where do the 9's end to make it 1?

How far down the line?

An infinite string of nines is not a number, it's a (unrealisable, idealised) written representation of a number. A number that, in this case, happens to be identical to 1.0..., or 1.0, or 1

Totally agree.

1.0 has a value. Adding zeros does not change the value.

0.999... has no final value.

1 is a number.

0.999... is not.

There's neither a practical nor a conceptual difference. 0.999... = 9 * 0.111... = 9 * 1/9 = 9/9 = 1.

9 * 1/9 immediately reduces to 1 by definition.

9 * 0.111... is an infinite operation that has no final value.

These are not the same thing.

 

[Jokodo]

Where do the 9's end to make it 1?

How far down the line?

They don't.

There are no nines in the number (represented bx) 0.999... There are nines only in its decimal representations. Your quesion "where do the 9's end" demonstrates a category error when applied to the number.

Totally agree.

1.0 has a value. Adding zeros does not change the value.

0.999... has no final value.

It doesn't have a "final" value, nor any "intermediate" value. It just has a value.

1 is a number.

0.999... is not.

There's neither a practical nor a conceptual difference. 0.999... = 9 * 0.111... = 9 * 1/9 = 9/9 = 1.

9 * 1/9 immediately reduces to 1 by definition.

9 * 0.111... is an infinite operation that has no final value.

These are not the same thing.

0.111... is the decimal notation of the same number represented by 1/9, or 9/81 in fractional notation. 9 * 1/9 = 9 * 0.11.. is true by definition every bit as much as any other step. Your failure to distinguish between numbers and their notation doesn't make them interchangeable.

 

[untermensche]

They don't.

There are no nines in the number (represented bx) 0.999...

I see nines.

That is saying there is an infinite string of them.

 

[Jokodo]

They don't.

There are no nines in the number (represented bx) 0.999...

I see nines.

That is saying there is an infinite string of them.

Still not even remotely talking about numbers here.

 

[DBT]

Is the presidential election of 2020 happening now?

Or is it a future event?

There is the now and there are past events and there are future events.

We are talking about past events, not the present.

Past events could not have been infinite.

You miss the point. the past was once here and now, the future - whatever happens - will be here and now.

There is no waiting for here and now to arrive. It doesn't matter if the Universe began 13.6 billion years ago or if it is cyclic and has always existed....it is always here and now at every point of its existence.

The conditions of here and now in relation to an observer being relative to physical conditions, objects, events, velocity, gravity, time/space, etc, etc....

 

[untermensche]

They don't.

There are no nines in the number (represented bx) 0.999...

I see nines.

That is saying there is an infinite string of them.

Still not even remotely talking about numbers here.

Then we are talking about some special magic you possess. The ability to make infinite processes complete.

1/1 = 1

1/0.9 does not.

1/0.99 does not

1/0.999 does not

At what point in the string of nines does 1/0.999... become 1?

 

[untermensche]

Is the presidential election of 2020 happening now?

Or is it a future event?

There is the now and there are past events and there are future events.

We are talking about past events, not the present.

Past events could not have been infinite.

You miss the point. the past was once here and now, the future - whatever happens - will be here and now.

That is exactly what I said.

The past are events that happened. That actually happened.

They could not have been infinite.

The number of changes in the past could not have been infinite.

An infinity is not something that can possibly be completed. The past is completed at every present moment.

Only the finite completes.

 

[DBT]

Is the presidential election of 2020 happening now?

Or is it a future event?

There is the now and there are past events and there are future events.

We are talking about past events, not the present.

Past events could not have been infinite.

You miss the point. the past was once here and now, the future - whatever happens - will be here and now.

That is exactly what I said.

The past are events that happened. That actually happened.

They could not have been infinite.

The number of changes in the past could not have been infinite.

An infinity is not something that can possibly be completed. The past is completed at every present moment.

Only the finite completes.

Nobody said that events are infinite. As I said; events, by definition, are finite. Events have a beginning, a middle and an end. Events do not exist in isolation. Events are part of a larger system. It is the larger system that existed before any particular event started, had a middle and ended. All current events are here and now. This here and now does not require waiting for regardless of how long the larger system has existed, perhaps eternally. It is always here and now.

 

[untermensche]

That is exactly what I said.

The past are events that happened. That actually happened.

They could not have been infinite.

The number of changes in the past could not have been infinite.

An infinity is not something that can possibly be completed. The past is completed at every present moment.

Only the finite completes.

Nobody said that events are infinite. As I said; events, by definition, are finite. Events have a beginning, a middle and an end. Events do not exist in isolation. Events are part of a larger system. It is the larger system that existed before any particular event started, had a middle and ended. All current events are here and now. This here and now does not require waiting for regardless of how long the larger system has existed, perhaps eternally. It is always here and now.

Finite events occur in finite time.

If the past is some amount of finite events then the time they occurred in was finite as well.

 

[DBT]

That is exactly what I said.

The past are events that happened. That actually happened.

They could not have been infinite.

The number of changes in the past could not have been infinite.

An infinity is not something that can possibly be completed. The past is completed at every present moment.

Only the finite completes.

Nobody said that events are infinite. As I said; events, by definition, are finite. Events have a beginning, a middle and an end. Events do not exist in isolation. Events are part of a larger system. It is the larger system that existed before any particular event started, had a middle and ended. All current events are here and now. This here and now does not require waiting for regardless of how long the larger system has existed, perhaps eternally. It is always here and now.

Finite events occur in finite time.

If the past is some amount of finite events then the time they occurred in was finite as well.

Doesn't follow. It's not known if the BB was the beginning of time or not. It is not known whether our universe is a part of a greater system, a multiverse, infinite space, etc, but there is nothing to exclude the possibility.

 

[untermensche]

Finite events occur in finite time.

If the past is some amount of finite events then the time they occurred in was finite as well.

Doesn't follow. It's not known if the BB was the beginning of time or not. It is not known whether our universe is a part of a greater system, a multiverse, infinite space, etc, but there is nothing to exclude the possibility.

It does follow.

Which is why all you can muster is an empty claim and no reason to think it does not follow.

Infinite time means infinite events which means infinite changes.

Infinite changes is like the positive integers. As defined there cannot be the possibility of reciting the all positive integers, you cannot reach the end, the final integer. Just as there can be no possibility of infinite changes ending as past changes are ended at the present.

If there was infinite time in the past that is like saying there were infinite changes that finished occurring at every present moment.

It is claiming an infinity completed.

A contradiction.

Only the finite completes.

 

[Jokodo]

Still not even remotely talking about numbers here.

Then we are talking about some special magic you possess. The ability to make infinite processes complete.

1/1 = 1

1/0.9 does not.

1/0.99 does not

1/0.999 does not

At what point in the string of nines does 1/0.999... become 1?

0.999... is not a process. It's not even the concept of a process. It's a number that happens to be demonstrably identical to 1.0 unlike any finite string of 9s after the point.

 

[untermensche]

Still not even remotely talking about numbers here.

Then we are talking about some special magic you possess. The ability to make infinite processes complete.

1/1 = 1

1/0.9 does not.

1/0.99 does not

1/0.999 does not

At what point in the string of nines does 1/0.999... become 1?

0.999... is not a process. It's not even the concept of a process. It's a number that happens to be demonstrably identical to 1.0 unlike any finite string of 9s after the point.

It can't be demonstrated to be equal to 1.

Some manipulations are done that erase an infinitely small difference. Slight of hands. Tricks.

Demonstrate it is identical to 1 without changing it or doing anything to it.

Show me where the 9's end.

 

[Jokodo]

0.999... is not a process. It's not even the concept of a process. It's a number that happens to be demonstrably identical to 1.0 unlike any finite string of 9s after the point.

It can't be demonstrated to be equal to 1.

Some manipulations are done that erase an infinitely small difference. Slight of hands. Tricks.

Demonstrate it is identical to 1 without changing it or doing anything to it.

Show me where the 9's end.

They don't. And that's exactly why it's the same. It's been demonstrated to you in at least three different ways in the last couple of weeks alone. If you want to call those proofs "tricks" or "slights of hand", it's up to you to show where they go wrong. If you can't, all you're doing is demonstrating that you have no clue what you're talking about.

You probably also believe that in a spherical coordinate system, 180° West and 180° East are 360° apart.

 

[untermensche]

0.999... is not a process. It's not even the concept of a process. It's a number that happens to be demonstrably identical to 1.0 unlike any finite string of 9s after the point.

It can't be demonstrated to be equal to 1.

Some manipulations are done that erase an infinitely small difference. Slight of hands. Tricks.

Demonstrate it is identical to 1 without changing it or doing anything to it.

Show me where the 9's end.

They don't. And that's exactly why it's the same. It's been demonstrated to you in at least three different ways in the last couple of weeks alone. If you want to call those proofs "tricks" or "slights of hand", it's up to you to show where they go wrong. If you can't, all you're doing is demonstrating that you have no clue what you're talking about.

You probably also believe that in a spherical coordinate system, 180° West and 180° East are 360° apart.

I showed you. You are claiming infinite operations complete.

9 * 1/9 immediately reduces to 1 by definition.

9 * 0.111... is an infinite operation that has no final value.

These are not the same thing.

Which is why you can't demonstrate anything without some transformation or by performing some operation chosen from left field..

We are talking about an infinite series.

It does not by magic change into something else.