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New Proof that 1 = .999999999 Repeating

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infinity is not a number.
Did you know that 0 is not a number either? Think about it. 1 apple != 1 orange, but
0 apples = 0 oranges.

 
Originally posted by: acadia11
I''m putting an end to this debate ..999999999R != 1, .999999999999R is approximately 1.

End of debate.

Semantics are important, sort of like 1 / infinity is not equal to 0, it is approximately 0.

And dependant upon the granularity of the comparison determines the outcome. Even computers work this way when comparing two numbers.
Click to expand...

One problem: When designing computers, each decimal number is represented by a sequence of bits. For example, 1=0001, 2 = 0010, 3 = 0011, so forth. You can also do 1 = 0001, 10 = 0100, 33 = 1111, etc. However, for the computer the bit sequence, 0001 can equal 1, 2, 5000, 33, 42, the letter a, the lettter A, the President of the United States, the size of your *****, lemon meringue pie, etc. Computers don't compare numbers. They compare bit patterns which are represented by voltage levels.

The topic of this thread is not an argument of semantics. It is a debate concerning the laws of mathematics and logical reasoning. In order to argue semantics, one must first assume that "1" and ".999..." are the same.

Common sense has little functionality in math or science, which are deeply rooted in logic. Common sense is subjective, being highly dependent upon the observer.
Common sense tells me the sun rises every morning and falls every evening. Common sense tells me that a metal weight will fall faster in vacuum than a feather of the same weight. Common sense tells me that Microsoft shouldn't be a monopoly if their product is so infamously unstable.

For a more entertaining read, I humbly ask for a proof that 1 + 1 = 2.
http://descmath.com/diag/nines.html started off with good potential. However, the white box after the first paragraph gave me a sinking feeling and the paragraph following the box confirmed said feeling. I enjoy reading good proofs of arguments counter to common thought, but this is definitely going off into left field.
 
For a more entertaining read, I humbly ask for a proof that 1 + 1 = 2.
Click to expand...

That one might be a little harder. 😛

http://descmath.com/diag/nines.html started off with good potential. However, the white box after the first paragraph gave me a sinking feeling and the paragraph following the box confirmed said feeling. I enjoy reading good proofs of arguments counter to common thought, but this is definitely going off into left field.
Click to expand...

I couldn't really get anything useful out of that. As noted above, intuition and "common sense" don't always get you very far in mathematics. However, I didn't really mention that the proof I gave above is only good for the real numbers. It is possible there are other number systems where you *can* define a number that is bigger than "0.999..." but smaller than "1.000..." -- but not with rational or real numbers, sorry.
 
Originally posted by: Matthias99
Originally posted by: darbius
Originally posted by: Lizabath
no you are wrong 91ttz,

.999... = 1

Take some advance math courses and you will find out why. 😛
Click to expand...


I've taken advanced math courses and that is just one of the few rules of math I'm not willing to accept. No matter which way you spin it or how many proofs you try to do, .999 repeating will never, ever equal 1.
Click to expand...

<snip>
Click to expand...

If you look up a few posts you'll see that I've provided a calc proof for this.

 
Originally posted by: venk
The difference between 1 and .9 is 1/10 or .1
The difference between 1 and .99 is 1/100 or .01
The difference between 1 and .999 is 1/1000 or .001

Therefore


The difference between 1 and .99999 Repeating is 1/infinity or 0

Therefore 1 = .99999 Repeating


CLIFFS
--------------
1-.9 = .1
1 - .99 = .01
1- .999 = .001
1 - .9999 Repeating = 0
Click to expand...
doh nm
 
Originally posted by: acadia11
I''m putting an end to this debate ..999999999R != 1, .999999999999R is approximately 1.

End of debate.

Semantics are important, sort of like 1 / infinity is not equal to 0, it is approximately 0.

And dependant upon the granularity of the comparison determines the outcome. Even computers work this way when comparing two numbers.
Click to expand...

HAHA you know this guy didn't take any college math. There is no approximate about it.
 
Originally posted by: venk
The difference between 1 and .9 is 1/10 or .1
The difference between 1 and .99 is 1/100 or .01
The difference between 1 and .999 is 1/1000 or .001

Therefore


The difference between 1 and .99999 Repeating is 1/infinity or 0

Therefore 1 = .99999 Repeating


CLIFFS
--------------
1-.9 = .1
1 - .99 = .01
1- .999 = .001
1 - .9999 Repeating = 0
Click to expand...


congrats dumbass. that's first year high school math
 
Originally posted by: cain
Originally posted by: venk
The difference between 1 and .9 is 1/10 or .1
The difference between 1 and .99 is 1/100 or .01
The difference between 1 and .999 is 1/1000 or .001

Therefore


The difference between 1 and .99999 Repeating is 1/infinity or 0

Therefore 1 = .99999 Repeating


CLIFFS
--------------
1-.9 = .1
1 - .99 = .01
1- .999 = .001
1 - .9999 Repeating = 0
Click to expand...


congrats dumbass. that's first year high school math
Click to expand...

I did that in junior high...

man, those were the days....
 
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