1. You asume there is an end, as shown in this statement/question: "In that case, what is 0.999...8 equal to? i.e. an infinite number of 9's with an 8 at the end."

However when you deal with infinity this is not the case.
0.999...8 equals 0.999...8 because it ends, thus does not continue infinitly. 2. Originally Posted by cpjust In that case, what is 0.999...8 equal to? i.e. an infinite number of 9's with an 8 at the end. That probably doesn't make much sense mathematically and maybe even logically, but then again, if 0.999... = 1, then that means 1.000...1 = 1 also right? and if you subtract 1 from that it leaves 0.000...1. If you then subtract that from 0.999... you get 0.999...8.
Just because it can be "proven" mathematically, doesn't necessarily mean it's true. It's just true as far as we can currently prove. This makes absolutely no sense whatsoever. Think about what you're saying, "an infinite number of 9's, with an 8 at the end"

But thanks for the laugh  3. The number 1 can be written as 0.999... just like it can be written as 1.000...
With that kind of mentality, it's almost like shorthand for a limit:

The difference between 1 and 0.99 is 0.01.
The difference between 1 and 0.99999 is 0.00001
So as you get 0.999999 gets infinitely close to 1, the difference gets infinitely close to 0.

The same applies as 1.00000001 gets infinitely close to 1.

All three representations (1, 0.999..., and 1.000...) are mathematically equal, they're just different ways that humans have expressed the number 1. Originally Posted by Kernel Sanders Well, 1/9 isn't actually equal to .111... because 1/9 is impossible to represent using base 10 if you get right down to it
It's impossible to represent 1/9 as a number in base 10 unless you have an infinite amount of 1's, which is usually what's meant by the ellipsis. 4. Originally Posted by Stonehambey This makes absolutely no sense whatsoever. Think about what you're saying, "an infinite number of 9's, with an 8 at the end"

But thanks for the laugh Well I did say it doesn't make much sense didn't I? I just invented (0.000...1) by subtracting (0.999...) from 1 5. but you still base your logic on the fact that 0.000...1 is a limited number, but it contains unlimited number of 0's so you would not be able to write a 1 at "the end" because there is no end, there are an unlimited amount of 0's. 6. Originally Posted by Shakti but you still base your logic on the fact that 0.000...1 is a limited number, but it contains unlimited number of 0's so you would not be able to write a 1 at "the end" because there is no end, there are an unlimited amount of 0's.
I know you can't write a 1 on the end on paper, but I'm just doing it in my head (and using ...1 to represent it) -- basically the smallest possible non-zero number. 7. basically the smallest possible non-zero number.
But if there was a smallest positive real number, then the set of real numbers is countable. 8. Originally Posted by laserlight But if there was a smallest positive real number, then the set of real numbers is countable.
There are an infinite number of numbers, regardless of whether they're natural, whole, integer, rational or irrational numbers, so I'm not sure what your point is?
If you could count forever, then it's countable.  9. There are an infinite number of numbers, regardless of whether they're natural, whole, integer, rational or irrational numbers, so I'm not sure what your point is?
My point is that if you give me the "smallest possible non-zero number", I can give you a smaller non-zero number, simply by dividing it by a number greater than 1. Clearly, there is no smallest non-zero number, or more accurately, there is no smallest positive real number. I assumed that you were aware of the concept of countable and uncountable sets, so I expressed my point indirectly.

If you could count forever, then it's countable.
If you can map a set (as in a one to one mapping, possibly with some natural numbers left unmapped as in the case of a finite set) to the set of natural numbers (or some other countable set), then that set is countable. 10. You aren't dealing with a technical infinity (.99999999999->) VS 1.(000000->). Although a large technicaly 9 != 10 therfore .9 != 1. You can just say a number is *.(infity zeros)1* larger then it is defined to be. .999(infinity 9's) is completely seperate from 1.(zero is defined in mathematics as no value, if you have zero objects you have no objects)

-- Subtracting these two numbers does not equal zero nor does adding them equal 2 * either number. No matter what you say to be true about these, you cant disreguard the fact that .9(infinity) does not equal one it equals very close to one, but not 1. Much in the same way 1.1 != 1.

There's nothing to accept, the statement that both number are the same is false, prehaps in the ideogy of infinity it could be said to have merit, but in such a case you shoulden't be comparing infinity with a real number anyway, as infinity is a hypothetical for "A point of undefined value ~ Something with no end" VS a whole number, which ends immediately after it's decimal (1.) You cant subtract infinity from this number and get a logical result, it merely becomes (1. - infinity) So why would you get a logical result when you substract (1 - .9(infinity 9s)) You're still dealing with infinity, you'll still get an illogical result.

Slightly offtopic though, neither 1 = 0 nor .999 = 1 are true in the realm of reality. (.999 apples != 1 apple!) (1 apple != 0 apples!) So there, my long winded rant is over. Enjoy :P 11. Originally Posted by laserlight My point is that if you give me the "smallest possible non-zero number", I can give you a smaller non-zero number, simply by dividing it by a number greater than 1. Clearly, there is no smallest non-zero number, or more accurately, there is no smallest positive real number. I assumed that you were aware of the concept of countable and uncountable sets, so I expressed my point indirectly.

If you can map a set (as in a one to one mapping, possibly with some natural numbers left unmapped as in the case of a finite set) to the set of natural numbers (or some other countable set), then that set is countable.
OK, let me start over... The number I was talking about with (0.000...1) is not a quantifiable amount. Maybe if I said (1/infinity) my point would be more clear, although after all this I think I forgot what my original point was anyways.  12. Originally Posted by Blackroot
No matter what you say to be true about these, you cant disreguard the fact that .9(infinity) does not equal one it equals very close to one, but not 1.
That is rubbish: 0.999... and 1 are symbols. Proofs have shown that the numbers represented by these symbols are the same. Originally Posted by Blackroot
prehaps in the ideogy of infinity it could be said to have merit, but in such a case you shoulden't be comparing infinity with a real number anyway
This is a strawman argument since the proofs in question do not involve treating the concept of infinity as a real number. Originally Posted by Blackroot
Slightly offtopic though, neither 1 = 0 nor .999 = 1 are true in the realm of reality. (.999 apples != 1 apple!) (1 apple != 0 apples!)
By that reasoning 0.5 + 0.5 = 1 is false is the "realm of reality" as well, since adding half an apple and another half an apple does not give you an apple. In any case, note that we are talking about 0.999..., not 0.999. Part of your problem is inaccuracy of notation, which also leads you to postulate that strawman argument as mentioned. 13. Well part of the problem comes from differeing definitions of infinity. In mathematical terms infinity is a fixed quantity that exists outside the set of real numbers. Most laymen think of it as a really large number'. Its not really large it is in fact unquantifiably large. It cannot be treated as so large that it simply obliterates all other values that are entangled with it, it must be treated as a unique quantity and kept serpate from the entangled terms, just as the imaginary number i must be treated as a seperate quantity, otherwise the maths break down.

5i * 5i yields 25i^2 = -25, not 25i

5 * infinity * 5 * infinity = 25 * infinity ^2, not 25 infinity or inifinty

5/0 = 5 * infinity not infinity

5/0 * 0 = 5

5*infinity * 0 = 5

If you do NOT treat infinity and hence division by zero as special unique quanities then the maths break down and in that illogical realm yes, you can prove any number to equal any other number, which is itself the proof that you must keep them seperate. 14. Code:
`Most laymen think of it as a really large number'. Its not really large it is in fact unquantifiably large.`
Lol, I would be a just a little bit surprised if I met anyone older than 10 that beleived that. 15. Originally Posted by abachler 5/0 * 0 = 5

5*infinity * 0 = 5
Shouldn't those both equal 0? Anything times 0 equals 0 right? Popular pages Recent additions 