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0.9999999999.... vs 1?
- Thread starter COMMUNIST FLISK
- Start date
Ozymandyus
New Member
Well, not really. There are rules for dealing with 0. Doesn't really break anything because if you follow the rules then you have no problems.
Master_Ghost_Knight
New Member
Never in math.GoodKat said:
Binary is one of the easiest systems to work whit, altough if you can convert from base 10 to base 2, technicaly there shouldn't be a problem converting to every other bases.blinddesign said:
I will give you an help if you start a topic.
Edit: I guess you already did.
Balanced Ternary is much easier to do mulitplication and division of large numbers than binary or decimal.
http://en.wikipedia.org/wiki/Balanced_ternary
and it`s fun too...
Th1sWasATriumph
New Member
Well, I clearly wasn't being entirely serious with my "prove anything with numbers" ass.
However, if maths is axiomatically true, how can one value be the same as another when they are different? Even if the difference is infinitely small, it's still a difference. 1 is a whole number, 0.9999 . . . is not, hence the decimal point. In real terms, it never actually meets 1.
It may be a bad idea to argue mathematics from the perspective of someone who thinks 2+5=rhombus, but still.
I mean, you could write 0.9999 . . . for billions of digits. It would never be one, however close it got. A similar sort of paradox, although it obviously isn't a paradox, is: take a triangle with a 1" base, the apex of which terminates 500,000 light years away. The angle of the terminating point (I have forgotten all my GCSE triangle nomenclature) would be so small to be practically unmeasurable, to all intents and purposes 0. Would you say it IS zero purely because it's very, very close?
Would you say this comparison is meaningless? I don't care. I always found it interesting in its own right.
However, if maths is axiomatically true, how can one value be the same as another when they are different? Even if the difference is infinitely small, it's still a difference. 1 is a whole number, 0.9999 . . . is not, hence the decimal point. In real terms, it never actually meets 1.
It may be a bad idea to argue mathematics from the perspective of someone who thinks 2+5=rhombus, but still.
I mean, you could write 0.9999 . . . for billions of digits. It would never be one, however close it got. A similar sort of paradox, although it obviously isn't a paradox, is: take a triangle with a 1" base, the apex of which terminates 500,000 light years away. The angle of the terminating point (I have forgotten all my GCSE triangle nomenclature) would be so small to be practically unmeasurable, to all intents and purposes 0. Would you say it IS zero purely because it's very, very close?
Would you say this comparison is meaningless? I don't care. I always found it interesting in its own right.
Master_Ghost_Knight
New Member
In analitical terms you cannot say that a number x is whole or not without a proper definition of what is a whole number and what isn't. A Whole number is a number that belongs to R+ (including 0) and that can be equal to the addition of another whole number +1 (neutral element of the multiplication), except for 0 that is whole by default. This comes directly from the extent of numbers that you can distinguish whit the axioms 0 is difrent from 1 and the sums of 2 bigger numbers is bigger then the sum of 2 smaller ones.Th1sWasATriumph said:
The problem is this is valid independently of the system you are trying to represent the number.
Our common decimal representation is a cascading system of a sequence of strings associated whit the power of a base b that cannot compensate for an infinite construction. But for a mathematical point of view, the way it is decided that such number is whole or not is not by looking at it at a faulty representation but by reconstructing the number in it's analytical form. So in analytical terms:
Th1sWasATriumph said:
is meaningless for the simple reason that you don't know what 0.99999... values, and thus cannot classify it to see in which category does it fall (until you reconstruct the numbe).
But it's not a billion nines. It's an infinite number of nines.
Yes the angle on the triangle is essentially zero, but it cannot be equal to zero. This follows from the definition of a triangle. It is not just that there is no practical difference between 0.(9) and 1, but there is actually no difference at all.
Yes the angle on the triangle is essentially zero, but it cannot be equal to zero. This follows from the definition of a triangle. It is not just that there is no practical difference between 0.(9) and 1, but there is actually no difference at all.
Th1sWasATriumph said:
You seem to fall in the same hole twice, because as Aught3 pointed out, it is not a billion decimals, it's an infinite number of 9s. While the triangle is quite a good comparison, it's flawed, try to think about a triangle with a base of 1'' that terminates an infinite amount of light years away. The whole problem I think, is that you're trying to think about this in terms of the real-world, math is something abstract and often quite counter-intuitive. (But it is NEVER ilogical
)felixthecoach
New Member
I have a few points to make that I feel God wants me to tell you.
1. I still dont believe in it because you have not shown me enough transitional numbers...
2. I have never seen a .9... give birth to a 1.
3. These numbers are so complex, only God could have created them that way.
4. 2 needs an Adder to make 3, just like a painting needs a painter. 1 can't come from .9... there has to be an Adder to "Add" the 0.0...01 that is added to the .9... to create a 1.
5. You guys are in a giant conspiracy with the rest of the math community to confuse my kids about math and make me out to be a religious nut.
6. I don't believe in infinitely recurring numbers.
1. I still dont believe in it because you have not shown me enough transitional numbers...
2. I have never seen a .9... give birth to a 1.
3. These numbers are so complex, only God could have created them that way.
4. 2 needs an Adder to make 3, just like a painting needs a painter. 1 can't come from .9... there has to be an Adder to "Add" the 0.0...01 that is added to the .9... to create a 1.
5. You guys are in a giant conspiracy with the rest of the math community to confuse my kids about math and make me out to be a religious nut.
6. I don't believe in infinitely recurring numbers.
blinddesign
New Member
felixthecoach said:
respect points to you for that.
Ozymandyus
New Member
As a example of MGK's point - the representation (3/1.5) can't be considered a whole number, until you actually perform the valuing action implied. But clearly it still equals 2, which is a whole number.
If you made a list of whole numbers, you wouldn't include (3/1.5) or (4/2) or whatever. You wouldn't even list 1.0 - we have multiple ways of expressing numbers in math, and this is just another one of them.
If you made a list of whole numbers, you wouldn't include (3/1.5) or (4/2) or whatever. You wouldn't even list 1.0 - we have multiple ways of expressing numbers in math, and this is just another one of them.
I'm very surprised how many people have difficulties with infinity...
1/INF is exactly 0
two parallel lines intersect at infinity
1 is equal to 1/2 + 1/4 + 1/8 + 1/16 + ... (which can be written as 0.11111... in binary)
0.9999... is just another way of writing 1, just like cos(0) or -e^(i*pi)
"There are sooo many gaps between 0.9999... and 1!!!"
1/INF is exactly 0
two parallel lines intersect at infinity
1 is equal to 1/2 + 1/4 + 1/8 + 1/16 + ... (which can be written as 0.11111... in binary)
0.9999... is just another way of writing 1, just like cos(0) or -e^(i*pi)
We really need a moderation system. 10 thumbs up!! :lol:felixthecoach said:
"There are sooo many gaps between 0.9999... and 1!!!"
Master_Ghost_Knight
New Member
:? I Wouldn't go that far. No.Pulsar said:
Ozymandyus
New Member
Can't be answered with the information given. What is x where x != 0?
There are degrees of infinity in math, if thats what you are asking, i.e. 2x infinity = infinity+infinity < 3xinfinity etc... even though its impossible to conceive intellectually, degrees of infinity work mathematically.
There are degrees of infinity in math, if thats what you are asking, i.e. 2x infinity = infinity+infinity < 3xinfinity etc... even though its impossible to conceive intellectually, degrees of infinity work mathematically.
Master_Ghost_Knight
New Member
The correct answer to this is undetermined. No one knows, in some cases it is one thing and in other it is something completly different.GoodKat said: