Is 1 = 0.9999......

[MadRat]

Originally posted by: Haircut
OK, I said back in February that I would no longer take part in this thread. I've stayed away for nearly 11 months, but I can refrain from posting no longer.

Madrat (and any others that believe they are two different values), can I ask you to tell me what is the last digit of 0.999...

At the inifinite position there is a digit of 9. The infinite position has no end (defined limit) or specific location, because its undefined. Since it has no end then we cannot express it without using some sort of notation such as ...

 

[MustangSVT]

this thread = 0.99999.....

 

[RossGr]

Originally posted by: MadRat
The same logic to say .999...=1 can be used to say .000...1 exists, but then that proves .999...<>1. How funny.

The logic is not the same. Your "number" is an infinite number of zeros followed by a 1, while the standard use as in .999... is an infinite number of 9s followed by another 9, in other words the 9s never end. Your usage has a end to infinity, 'cuz the 1 is at the "end" of infinity.

I, and others, say that infinity means "does not end" so by this definition your 1 can never be placed.

We have been through this at least 5 times, yet you continue to post your beliefs. As soon as you can wrap your head around the correct concept of infinity we will be able to move on.


You are simply wrong, your beliefs do not constitute defined truth.

 

[Thraxen]

Meh.. 0.999.... is not a value that can be attributed to anything "real" to begin with. Everything has a finite value. You only end up with values like this on paper. 1 can be attributed to something real. I can hold 1 apple in my hand, but I can't hold 0.999... apples in my hand. That's why those two number can only be considered the same on paper. This is a stupid debate.

 

[RossGr]

Originally posted by: Thraxen
Meh.. 0.999.... is not a value that can be attributed to anything "real" to begin with. Everything has a finite value. You only end up with values like this on paper. 1 can be attributed to something real. I can hold 1 apple in my hand, but I can't hold 0.999... apples in my hand. That's why those two number can only be considered the same on paper. This is a stupid debate.

What is stupid is people who step into a disscussion of the Real Number system with no knowledge of what the Real Number system is. The Insane Rodent being one and ....

 

[Thraxen]

What is stupid is people who step into a disscussion of the Real Number system with no knowledge of what the Real Number system is. The Insane Rodent being one and ....

LOL... OK. But you get my point, right? 0.999... only exists on paper. It's not a "real" value. It may part of the Real Number system, but it's not a value that can be attributed to anything that actually exists.

 

[Chu]

Originally posted by: Thraxen

What is stupid is people who step into a disscussion of the Real Number system with no knowledge of what the Real Number system is. The Insane Rodent being one and ....

LOL... OK. But you get my point, right? 0.999... only exists on paper. It's not a "real" value. It may part of the Real Number system, but it's not a value that can be attributed to anything that actually exists.

A. 0.9999... = 1
B. I can hold 1 apple in my hand, so it is more real then 0.999... since I can't hold 0.999... apples in my hand.


-Chu

P.S., I know what your trying to get at . . . that we create objects in math that don't have correspondance to things in real life. This is not necessarly a flaw, and many things that we once thought have no correspondance to things in real life (imaginary numbers and non-eucledian gemoetry are the first that come to mind) turned out to have important signifinance later. In general though, most mathematicians don't really care if their work has any signifiance to the real world.

 

[Thraxen]

I can hold 1 apple in my hand, so it is more real then 0.999... since I can't hold 0.999... apples in my hand.

It still only exists on paper. Or is that wrong?

 

[silverpig]

Originally posted by: Thraxen
Meh.. 0.999.... is not a value that can be attributed to anything "real" to begin with. Everything has a finite value. You only end up with values like this on paper. 1 can be attributed to something real. I can hold 1 apple in my hand, but I can't hold 0.999... apples in my hand. That's why those two number can only be considered the same on paper. This is a stupid debate.

Uh, no.

The ratio of the length of a ruler to the length of itself is exactly 0.999... That's perfectly "real" and has been attributed to something.

 

[Thraxen]

The ratio of the length of a ruler to the length of itself is exactly 0.999... That's perfectly "real" and has been attributed to something.

Ratios are different. You are just dividing one real value by another real value. But the result is not a physical thing. Can't hold a ratio. I was talking about something physically real. I'm not saying that any of what you guys are saying is wrong, not at all. I just find it funny to be arguing about a number that can only exist on paper.

But here is a real question... just because I want to understand this debate better. 0.999... is not a finite value, right? Because there will always be another '9'. So how can a value that is not finite be equal to a value that is?

 

[Hector13]

Originally posted by: Thraxen

What is stupid is people who step into a disscussion of the Real Number system with no knowledge of what the Real Number system is. The Insane Rodent being one and ....

LOL... OK. But you get my point, right? 0.999... only exists on paper. It's not a "real" value. It may part of the Real Number system, but it's not a value that can be attributed to anything that actually exists.

when was the last time you held -1 apples in your hand?

 

[Chelsey]

No it isn't. It depends on what you're using it for, but in reality it isn't.

 

[mchammer187]

Originally posted by: Thraxen

The ratio of the length of a ruler to the length of itself is exactly 0.999... That's perfectly "real" and has been attributed to something.

Ratios are different. You are just dividing one real value by another real value. But the result is not a physical thing. Can't hold a ratio. I was talking about something physically real. I'm not saying that any of what you guys are saying is wrong, not at all. I just find it funny to be arguing about a number that can only exist on paper.

But here is a real question... just because I want to understand this debate better. 0.999... is not a finite value, right? Because there will always be another '9'. So how can a value that is not finite be equal to a value that is?

it has an infinite number of digits

that does not mean it is not finite

finite means not infinite and sure you are not going to say the .999 r is infinite IE a very large number that has no upper bound

large number of digits does not mean large number obviously

.99999999999r = 1 so it is finite

 

[RossGr]

The greatest utility of mathematics is its ability to deal with concepts which may or may not correspond to physical entities. In the past there has been mathematical paths explored which had no apparent physical meaning. One good example is Riemann's work in non Euclidean Geometry. It had no apparent use, until Einstein came along and made such ideas the corner stone of General Relativity. Currently Mathematics is driving String Theory, there is as yet no Physical evidence which gives rise to this theory it is only Math, so simply because something cannot be held in your hand is not reason to dismiss it as not worth while.

Of course .999.... cannot be expressly written but we must be able to handle such concepts in order to fully understand the Real number system. Consider this

Take the number line between 0 and 1, subdivide it into 10 boxes, number each box starting with 0 for the first box and 9 for the last. Now go to the last box, the 9th, and repeat the process, subdivide the region between .9 and 1 into 10 boxes label each 0 thru 9, now the last box will be labled .99 subdivide it into 10 boxes. Can you see where this is going? I can repeat this process forever there is no end to it, yet the right hand box will always exist with 1 being the right hand end point. The boxes will always be smaller but will never end. This is a construction of the number line. Every number in the first box starts with a 0 ie .0, every number in the second box starts with a 1 ie .1 etc.

Now I can conceive of this process, therefore we must make an effort to deal with it, what, if any, value does .999... have? Is it a fixed point on the number line? These are questions that Mathematicians ask.

If you consider the Set of Russian Doll boxes I described above you can clearly see that .999... has to be less then or equal to 1. Clearly it is not greater then 1. Simply because I have constructed it that way. We can also say that .999... is greater then any finite number of 9s again because it is constructed that way. So .999... is greater then any finite number of 9's and less then or equal to 1. I say that is less then or equal to one, because at this point I have only my construction to work with, .999... must be less then 1, or equal to 1 or greater then one. That is an exhaustive list of the possibilities. I can rule out only the last, it cannot be greater then 1, the other 2 remain.

It is the very fact that .999... cannot be written that forces it to be the same as 1. Any string of 9's which can be written is different from 1 that which cannot is a representation of 1.

 

[MadRat]

Originally posted by: Hector13
when was the last time you held -1 apples in your hand?

What about your bank account?

 

[Howard]

Originally posted by: MadRat

Originally posted by: Hector13
when was the last time you held -1 apples in your hand?

What about your bank account?

The value that the bank stores isn't physical...

 

[OokiiNeko]

RossGR,
Deep in this thread, I linked to a number of "great" mathematicians who have said that infinity and the real number system do not play well together, if at all.

While this thread was interesting for awhile, and educational for me, your condescending attitude towards those people here who believe .999r does NOT =1 has worn thin.

Bottom line is no one knows for sure what happens at infinity, not even you.


P.S. Happy New Year to all.

 

[RossGr]

Originally posted by: OokiiNeko
RossGR,
Deep in this thread, I linked to a number of "great" mathematicians who have said that infinity and the real number system do not play well together, if at all.

While this thread was interesting for awhile, and educational for me, your condescending attitude towards those people here who believe .999r does NOT =1 has worn thin.

Bottom line is no one knows for sure what happens at infinity, not even you.


P.S. Happy New Year to all.

I do not recall your links. Great? Perhaps before Cantor? As far as I know the rules are now pretty well worked out, infinity and the Reals coexist quite nicely.

Sorry if you are not happy with my frustration at those who post as if they knew about this matter, when it is clear they do not even know what there is to know about it. You can choose to open thread or not. Perhaps you should choose not to open it.

 

[TommyVercetti]

yes

 

[MadRat]

Originally posted by: Howard

Originally posted by: MadRat

Originally posted by: Hector13
when was the last time you held -1 apples in your hand?

What about your bank account?

The value that the bank stores isn't physical...

But you can have deficits. A better example may be waveforms.

 

[godspeedx]

Originally posted by: Howard

Originally posted by: MadRat

Originally posted by: Hector13
when was the last time you held -1 apples in your hand?

What about your bank account?

The value that the bank stores isn't physical...

A number doesn't have to be physical in order to be defined as a number.

 

[Hector13]

Originally posted by: godspeedx

Originally posted by: Howard

Originally posted by: MadRat

Originally posted by: Hector13
when was the last time you held -1 apples in your hand?

What about your bank account?

The value that the bank stores isn't physical...

A number doesn't have to be physical in order to be defined as a number.

that was the whole point of my post.

 

[Skyclad1uhm1]

I'm bored.

 

[RossGr]

Originally posted by: Skyclad1uhm1
I'm bored.

We've seen that link. Not clear to me what use it is.

 

[Kyteland]

Hmm....

One whole year.

Has it really been that long?