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Is 1 = 0.9999......
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SilentRunning
Golden Member
Ain't gonna happen. 😛
MadRat
Lifer
If .999... can exist then so can a difference between 1 and that number. The problem is that the same people that insist that .999... does exist are the same ones that say it can be represented. Unfortunately .999... cannot be represented on the number line meaning then it doesn't exist. At the same time if you accept that .999... does exist then there must be a difference between 1 and that number. To say that they are the same is a copout because to define .999... as anything but 1 means a difference exists. By the definition of .999... it does not equal 1 and therefore there must be a difference bewteen them. Since you claim that no difference exists (because you say that .999...=1) then it also means the .999... value also does not exist. Philosophically and by your own rules .999... either realistically neither does exist or they ideally (being .999... and the difference of 1-.999...) both exist, therefore its a pointless argument. The argument leaves mathematics and becomes one of philosophy.
You cannot have it both ways.
spyordie007
Diamond Member
yes, and it was long before this thread ever came into existance.
In the rules of mathmatics ".99999...." is exactly the same thing as "1", we could easily talk about other ideas and theories where we are unsure as to whether the number "1" exists all day however based upon the rules of mathmatics the answer is simply a resounding "yes".
If you want to startup your own theorm of mathmatics I eagerly await the book (it should be quite interesting to see the similarities and differances between the currently accepted rules of mathmatics) however my answer of "yes" is based upon the currently world-wide accepted rules of mathmatics, both what I learned in calculus and in "real life".
-Spy
spyordie007
Diamond Member
You are right in that you cannot have it both ways, the problem is that you believe the definition of .999.... does not equal 1 which leads me to believe that you never got into higher level math.
It's not that I want to make this any more of a "flame war" but this is going to be a hard concept for those who have never worked in higher math, particularly calculus where the concept of limits is introduced. In fact the most conclusive proof that 1 = 0.9999...... is lim x -> infinity of 1-1x10^-x so please don?t take it personally if some people get aggravated when you tell them otherwise. If someone came up to you and told you that you were wrong about something you knew to be absolutely true you would also feel a little threatened. I don?t want to say that you are "dumb" but please accept that there are people here with a higher level of math skills and they have conclusive proof that 1 = 0.9999......
-Spy
EDIT: view ViperGTS's post above mine for a much better representation of the "limits" equation proving that the answer is still "yes".
spyordie007
Diamond Member
Of course, and there is always the 3(1/3)=3*.3333...=.9999....=1 equasion that shows it with simple fractions. I was just saying that the concept becomes much easier to under stand as you begin to understand concepts such as limits (as you learn limits it is easier to understand why 1/3 is exactly equal to .333.... and that .999.... is exactly equal to 1).
-Spy
MadRat
Lifer
No, you ignore logic to make your equations work. If you take any number and times it by a product of two you'll end up with an even result. You've only shown how to make .333... into 1/3 with hocus pocus of using a limit as the definition of the product to gain an even numbered product, which cannot happen. You cannot add three equal values to define an even product because that product does not exist; every product of 3 will equal an odd numbered result.
The answer lies before the limit, not at the limit. The limit lay outside your product by definition. Its the arrogance of this whole argument that the limit=product that is absurd. If .999... can exist then a number can exist between 1 and it. Since it cannot by your definition of the limit then that means neither exists. If you insist that .999... does exist then you have to accept the difference between 1 and .999... is possible, too.
You cannot have it both ways.
spyordie007
Diamond Member
madhat-
If they were terminating decimals you would be correct in assuming that their product would end with an odd number. Once more you would also be correct in that there could be something "between" ".999...." and "1". However .999... is not a terminating decimal and therefore cannot be treated as such.
The problem is that you are missing an important part in your understanding of the underlying concept and simply assuming that because something is true for ".999" and ".99999999" that it is true of ".999...". I'm not trying to get you to change your mind, I'm simply asking that you keep your mind open because some of these concepts are hard to understand. You cannot use newtonian physics to define relitivity, you have to learn a new set of rules otherwise it simply does not "work".
-Spy
If they were terminating decimals you would be correct in assuming that their product would end with an odd number. Once more you would also be correct in that there could be something "between" ".999...." and "1". However .999... is not a terminating decimal and therefore cannot be treated as such.
The problem is that you are missing an important part in your understanding of the underlying concept and simply assuming that because something is true for ".999" and ".99999999" that it is true of ".999...". I'm not trying to get you to change your mind, I'm simply asking that you keep your mind open because some of these concepts are hard to understand. You cannot use newtonian physics to define relitivity, you have to learn a new set of rules otherwise it simply does not "work".
-Spy
You (and many others in this thread) are having trouble with the concept of an infinitely repeating decimal.
Yes, if you stop at ANY point before infinity you end up with something less than one. Conventional math cannot deal with this, you'll sit there for eternity watching the 9's go by waiting for your chance to evaluate it.
However, you have been given the tools to deal with such a problem (namely limits, infinite sums, etc.).
If you are not familiar with the use of such tools, don't assume those who know them are wrong.
Viper GTS
SilentRunning
Golden Member
Yep, that someone is you.
lim [1- 10(-n)] as n --> inf
does not equal
[1 - 10(-n)] as n --> inf
SilentRunning
Golden Member
Why are you replying to my tag line? Can't you read? 😀
MadRat
Lifer
My age and training are irrelevant. The arguments you have were unsound and I have yet to question your age because its irrelevant. If you are insecure about the reasons behind the answer you cite then perhaps you shouldn't be in the argument in the first place. I'm am quite content that my argument is on solid ground and cannot be disproven.
Numbers follow constant laws. The argument for .333...=1/3, Viper, does not follow the constant that any product of 3 will equate to an odd number. The argument that .999...=1 also does not follow sound mathematical constants, therefore it must not be true. There is an equal likelihood that either the .999... does or does not exist, both arguments in which case neither would be equal to 1 by definition.
Numbers follow constant laws. The argument for .333...=1/3, Viper, does not follow the constant that any product of 3 will equate to an odd number. The argument that .999...=1 also does not follow sound mathematical constants, therefore it must not be true. There is an equal likelihood that either the .999... does or does not exist, both arguments in which case neither would be equal to 1 by definition.
Ahh.... Leave it to Mudrat to claim falsehood of basic mathematics with totally unsubstanticated claims, it is obvious to him, therefore it is god given fact. To Matrat ignorance is the final and end all argument.
What do you mean I want it both ways? There is only one possible way. Since I can concieve of .99... exitsting, it exists, seems that ought to be right down your ally, being philosophical and all. It has a fixed postion on the real number line which corresponds to the postion occupied by 1. Sorry if you do not like the fact that we have several representations for the same point on the number line, this is just a basic fact. All rational numbers have multilple representations. A rational number is any number which can be represented as a ratio of 2 integers, these numbers are charaterised by having either a terminating decimal representation like 1/2 = .5 or a infinitly repeating pattern like 1/3 = .33.... . By this definition .99... qualifies as the decimal representation of a rational number, that number is 1.
Matrat being a selfstyled philosopher (his calims, I have seen nothing of substance from him ) seems to feel that since no qualifcations are necessary to be a philosopher the same is true in all fields and that he is uniquely qualified to have final judgement because he has no qualifactions.
This simply is not the way it works, the real number line is man made. Real numbers exist only as tool invented by man, the men who invented and construted this tool were mathematicians, this is our toy and we know how it works. The only valid mathematical statement Matrat is capable of is "I DO NOT KNOW" , I surely would like to hear him say it.
What do you mean I want it both ways? There is only one possible way. Since I can concieve of .99... exitsting, it exists, seems that ought to be right down your ally, being philosophical and all. It has a fixed postion on the real number line which corresponds to the postion occupied by 1. Sorry if you do not like the fact that we have several representations for the same point on the number line, this is just a basic fact. All rational numbers have multilple representations. A rational number is any number which can be represented as a ratio of 2 integers, these numbers are charaterised by having either a terminating decimal representation like 1/2 = .5 or a infinitly repeating pattern like 1/3 = .33.... . By this definition .99... qualifies as the decimal representation of a rational number, that number is 1.
Matrat being a selfstyled philosopher (his calims, I have seen nothing of substance from him ) seems to feel that since no qualifcations are necessary to be a philosopher the same is true in all fields and that he is uniquely qualified to have final judgement because he has no qualifactions.
This simply is not the way it works, the real number line is man made. Real numbers exist only as tool invented by man, the men who invented and construted this tool were mathematicians, this is our toy and we know how it works. The only valid mathematical statement Matrat is capable of is "I DO NOT KNOW" , I surely would like to hear him say it.
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