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What if anything anyone has said leads you to an assumption that people are looking for a "last number" in a decimal that clearly is on going (eternal, forever, infinitely, whatever the term for endless in general you want to nitpick about concerning definitions) and still not so clearly equal to one _ pretty damn close by a constantly narrowing margin but still not 1 this .9 thing is a bit of mystery otherwise until someone figures out a way to express it accurately. You speak as if all the rules of numbers have been established and there is nothing that's going to change them. This is a case of an anomaly where no solid rule has been figured out so for sheer laziness on the part of mathematicians for the time being 1=.9(and so on) for practical purposes.

It has been proven

This is no anomaly.

This exercise is getting to the basics of what is the definition of what a rational number is plain and simple. It is not "laziness" by any means

In other words, if one cant understand that .9 repeating =1, than they don't understand the very definition of a rational number
 
It has been proven

I don't see how you are confused to be honest

This is no anomaly.

This exercise is getting to the basics of what is the definition of what a rational number is plain and simple

Not proven just supported, like a theory, all it has is data supporting it for now, and like any theory is not immune to becoming falsified by further research at some point should it become possible. Speaking of such things in a case closed fashion does no justice to progress pushing this topic toward that ugly little "D" word I prefer not to use.
 
Not proven just supported, like a theory, all it has is data supporting it for now, and like any theory is not immune to becoming falsified by further research at some point should it become possible. Speaking of such things in a case closed fashion does no justice to progress pushing this topic toward that ugly little "D" word I prefer not to use.

It is proven. It is not a "theory"

As I said, this is the very definition of what a rational number is.

Propeties of a rational number
The set \mathbb{Q}, together with the addition and multiplication operations shown above, forms a field, the field of fractions of the integers \mathbb{Z}.

The rationals are the smallest field with characteristic zero: every other field of characteristic zero contains a copy of \mathbb{Q}. The rational numbers are therefore the prime field for characteristic zero.

The algebraic closure of \mathbb{Q}, i.e. the field of roots of rational polynomials, is the algebraic numbers.

The set of all rational numbers is countable. Since the set of all real numbers is uncountable, we say that almost all real numbers are irrational, in the sense of Lebesgue measure, i.e. the set of rational numbers is a null set.

The rationals are a densely ordered set: between any two rationals, there sits another one, in fact infinitely many other ones. Any totally ordered set which is countable, dense (in the above sense), and has no least or greatest element is order isomorphic to the rational numbers.

Emphasis mine

By using the very definition of a rational number, if .99999 and 1 are not identical, there must exist another rational number between them. There isn't, and by that fact, and that alone, they must be the same

It is not even questioned in the field of mathematics if .9999repeating=1 or not. It's more of a conceptual notion that tests if people understand the defintion of what exactly a rational number is


I am not making this up, I am giving you mathematical definitions that prove they are identical.
 
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Here is a scenario for you to help you understand

Do you agree that 5 and 6 are separate rational numbers?

Yes, obviously but why?

Because there are an infinite amount of rational numbers seperating them, such as 5.5, 5.2, 5.1, 5.1111, etc.


Now take .99repeating and 1

Show me a number that is between .999repeating and 1.

You can not. As a result, they by defintion, are equal

The only way they cannot be the same is if you could find a number that is between them which can not be done

going back to an earlier post you had
Then is .8888infinity the same as .99999infinity? therefore .8888888infinity equals .99999999infinity? Since there is no number in between?

yes, clearly 0.9 is in between. As is .91, .92, .921345, , .9222222222, and an infinite amount of others

there is not however, anything between .9999999repeating and 1
 
It is proven. It is not a "theory"

As I said, this is the very definition of what a rational number is.

Propeties of a rational number


Emphasis mine

By using the very definition of a rational number, if .99999 and 1 are not identical, there must exist another rational number between them. There isn't, and by that fact, and that alone, they must be the same

It is not even questioned in the field of mathematics if .9999repeating=1 or not. It's more of a conceptual notion that tests if people understand the defintion of what exactly a rational number is


I am not making this up, I am giving you mathematical definitions that prove they are identical.

OK of course that is all this math based on a standard of ten symbols for single digit whole numbers we assume is a universal standard? (i think this is called base 10 but I may be incorrect here I'm rusty)perhaps there is a rule involving other standards that applies to what in this standard is freakish and causes these arguments we're having here with our system. I'm thinking about that dude a few posts back talking about "Contact" and recalling something I read once (not clear where) about how non-universal our standard may actually be, not once have I ever encountered mathematics outside our system in my daily life just more complex ways of manipulating it within the limits of those ten digits. Of course there is binary code and other standards with less digits. The problem here of course would be switching over to another standard (kind of like switching from standard measurement to metric in construction to give a rough analogy) What if under another base system this is not a problem and can clearly define the difference between the two in this system and given an equation to translate between the standards (kind of like calculating degrees F to and from Degrees C does) could show they are different?
 
What if anything anyone has said leads you to an assumption that people are looking for a "last number" in a decimal that clearly is on going (eternal, forever, infinitely, whatever the term for endless in general you want to nitpick about concerning definitions) and still not so clearly equal to one _ pretty damn close by a constantly narrowing margin but still not 1 this .9 thing is a bit of mystery otherwise until someone figures out a way to express it accurately. You speak as if all the rules of numbers have been established and there is nothing that's going to change them. This is a case of an anomaly where no solid rule has been figured out so for sheer laziness on the part of mathematicians for the time being 1=.9(and so on) for practical purposes.

I'm trying to be polite here, but at this point, you're way off the rails and the things that you're writing make no sense. It's obvious at this point that you don't understand the underlying mathematics. I also won't argue mathematics with someone who doesn't understand what constitutes a mathematical proof.

Not by our common system believing they are the same doesn't necessarily make them the same.

This statement speaks very clearly to your level of understanding. 0.(9) is another way to write "1." This is a very useful concept for dealing with curved lines. Another way to write 1 would -cos(pi).

Or better yet, -(e^i(pi)).
 
Duke: Between the two there is something, it's undefined but there is something just because we have no "number" as a symbol for it doesn't make it any less probable that they are two separate numbers. Signal:I am not saying that anyone here is a bad mathematician because I mention laziness--of course by definition .9'whatever' =1 as my last instructor stated by definition and we went over all the exercises and proofs concerning this in our coursework but he also stated they are not equal in the sense that working the problem out is a waste of time better spent on math that can be applied to our reality (this from a gentleman who started learning calculus before the days of the pocket calculator, doing everything by a wooden slide rule) he went on to state that mathematicians are lazy (not my words)and who knows when or if a solution will be discovered resolving this issue, but you're taking such comments personally when it is merely criticism of a tiny flaw in a concept that has been taught and assumed to be perfect.
 
OK of course that is all this math based on a standard of ten symbols for single digit whole numbers we assume is a universal standard? (i think this is called base 10 but I may be incorrect here I'm rusty)perhaps there is a rule involving other standards that applies to what in this standard is freakish and causes these arguments we're having here with our system. I'm thinking about that dude a few posts back talking about "Contact" and recalling something I read once (not clear where) about how non-universal our standard may actually be, not once have I ever encountered mathematics outside our system in my daily life just more complex ways of manipulating it within the limits of those ten digits. Of course there is binary code and other standards with less digits. The problem here of course would be switching over to another standard (kind of like switching from standard measurement to metric in construction to give a rough analogy) What if under another base system this is not a problem and can clearly define the difference between the two in this system and given an equation to translate between the standards (kind of like calculating degrees F to and from Degrees C does) could show they are different?


sorry but if your argument is based off a movie i really dont know what else to say

If you actually take time to research it, you will see that the base has nothing to do with this.

Mathematics is completely independent of base
Not by our common system believing they are the same doesn't necessarily make them the same.


They ARE the same. Why are you refusing to understand the very definition of what constitutes a rational number?


Duke: Between the two there is something, it's undefined but there is something just because we have no "number" as a symbol for it doesn't make it any less probable that they are two separate numbers.

There is nothing between them. Thats the concept of .(9) going on for infinity

I have provided you mathematical proofs and definitions.

You have provided me your opinion and an argument based off a science fiction movie. You need to do better than that
Signal:I am not saying that anyone here is a bad mathematician because I mention laziness--of course by definition .9'whatever' =1 as my last instructor stated by definition and we went over all the exercises and proofs concerning this in our coursework but he also stated they are not equal in the sense that working the problem out is a waste of time better spent on math that can be applied to our reality (this from a gentleman who started learning calculus before the days of the pocket calculator, doing everything by a wooden slide rule) he went on to state that mathematicians are lazy (not my words)and who knows when or if a solution will be discovered resolving this issue, but you're taking such comments personally when it is merely criticism of a tiny flaw in a concept that has been taught and assumed to be perfect.


There is no flaw in the concept. It's a definition

Your instructor seems incompetent if he is unable to come to terms with this.

By the way, many people have learned calculus before the calculator. Hardly gives him any "superior" credibility just as a fyi
 
sorry but if your argument is based off a movie i really dont know what else to say
Not based on a movie I stated essentially that the mention of the movie reminded me of an issue with mathematics that ours may not be as universal a language as we think (the movie uses the assumption that it is universal for the plot--Sagan needed a device to help tie the story together in this instance), not that I got it from the flick you might be over-analyzing things just a bit here.
 
Not based on a movie I stated essentially that the mention of the movie reminded me of an issue with mathematics that ours may not be as universal a language as we think (the movie uses the assumption that it is universal for the plot--Sagan needed a device to help tie the story together in this instance), not that I got it from the flick you might be over-analyzing things just a bit here.

You earlier wanted proofs, which were supplied, along with mathematical definitions, showing how they are the same.

You use opinion and a vague notion from a scifi movie for your argument yet seem to accept that over proof..

You have yet to provide ANY evidence stating otherwise (but demand proof for the counter argument, which was given), yet still cling to the notion you are correct...why?

You can start with evidence showing this issue you speak of. I want proofs, not "opinions" with no supporting evidence:cool:
Not based on a movie I stated essentially that the mention of the movie reminded me of an issue with mathematics that ours may not be as universal a language as we think
 
Wow I just wasted 30 mins of my life reading this, and I still do not understand it. Now Im not exactly stupid but this is so over my head.:D
 
1.99999...9 = 2. /end thread.

They are mathematically equivalent, this is first year University maths, and has been rigorously proven.

The reason is because you cannot find a rational number (i.e. a fraction) between 1.99999...9 (to infinity) and 2, and between any two distinct real numbers you can always find a rational number (as is explained here).

You earlier wanted proofs, which were supplied, along with mathematical definitions, showing how they are the same.

Exactly. To be honest I don't see how you can argue with mathematical proofs. They make even evolution or gravity look like flaky theories in comparison.
 
I thought of a math problem which probably has been chewed through before, but still...

So, a man sits in his car, 100 miles from his destination. His car goes exactly the distance to his destination per hour, so when he's 99 miles away from point B, he goes 99 mph only, and so forth. Keep in mind that he's constantly getting slower*, not breaking down from 100 to 99 mph, so when the distance is 99.3 miles for examples, the car goes 99.3 mph.

Q. Will he ever reach his destination? (* he would if he would drive the last mile with one mph, that's why I added the clarification)


This is somewhat similar to a short story by either Asimov or Dick I read some time ago, where a scientist in a tube gets shrunk more and more...
 
Here is a scenario for you to help you understand

Do you agree that 5 and 6 are separate rational numbers?

Yes, obviously but why?

Because there are an infinite amount of rational numbers seperating them, such as 5.5, 5.2, 5.1, 5.1111, etc.


Now take .99repeating and 1

Show me a number that is between .999repeating and 1.

You can not. As a result, they by defintion, are equal

The only way they cannot be the same is if you could find a number that is between them which can not be done
That would then imply that 0.99.. is not a number, but merely represents an unknown number. Therefore they cannot be equal.
 
I thought of a math problem which probably has been chewed through before, but still...

So, a man sits in his car, 100 miles from his destination. His car goes exactly the distance to his destination per hour, so when he's 99 miles away from point B, he goes 99 mph only, and so forth. Keep in mind that he's constantly getting slower*, not breaking down from 100 to 99 mph, so when the distance is 99.3 miles for examples, the car goes 99.3 mph.

Q. Will he ever reach his destination? (* he would if he would drive the last mile with one mph, that's why I added the clarification)


This is somewhat similar to a short story by either Asimov or Dick I read some time ago, where a scientist in a tube gets shrunk more and more...

I think so, but he might need to get out of his car at the end to push it over the line.
 
Nothing can move!

If an object moves from point A to point B, it must have been in motion for some length of time, starting at time S and ending at time T. But it can't actually move during that time period because at any given instant between S and T it is not moving. Why? Because an instant is an arbitrarily small lengthlof time during which we can take a snapshot and see that the rate of speed is zero.

Mathematically: We know that distance = speed x time. For any speed and positive number N that you specify, I can make sure the instant (time) is short enough so that distance will be less than N. Therefore, distance (which is a physical measurement so it must be non-negative) is smaller than any positive number. Hence distance is 0 at any instant.

No matter how many zeros you sum (even an infinite number of them) you still get zero. We know that the object is not moving at any given moment (instant). So across all moments from time S to time T, the object has not moved.

And with that I have proved why the cars on the 405 Freeway in Los Angeles never move!
 
2 x 17 = 34

1.999999999999 x 17 = 33.9999999999998

Those two aren't equal, thus 2 =/= 1.9999...infinity. Am I missing something here?
 
2 x 17 = 34

1.999999999999 x 17 = 33.9999999999998

Those two aren't equal, thus 2 =/= 1.9999...infinity. Am I missing something here?

Er, yes...you missed the fact that 1.999999999999 is not at all the same thing as 1.99999...9. You just rounded it off, and made a different number.

--Eric
 
2 x 17 = 34

1.999999999999 x 17 = 33.9999999999998

Those two aren't equal, thus 2 =/= 1.9999...infinity. Am I missing something here?

Yes, but:

http://xkcd.com/386/

This thread really surprises me. I learned this stuff in 9th grade. It's stuck with me ever since. I went to a pretty good school, but surely you folks learned this kind of math at some point in high school? Or even college?
 
Yes, but:

http://xkcd.com/386/

This thread really surprises me. I learned this stuff in 9th grade. It's stuck with me ever since. I went to a pretty good school, but surely you folks learned this kind of math at some point in high school? Or even college?

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