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[PTTG??]

If X is an integer; (not necessary, but neater for examples)

Y > X
Z > Y

Thus, we know that Z > X ... but what is the smallest possible value for Z relative to X?

For instance, X = 1
Thus, Y is at least 1.000...1, or otherwise 1+(1/inf.). Since Z is likewise (at very least) infinitesimally larger than Y, does that make it 1.000...2? 1+(2/inf.)?

[Angellus]

Yes, that seems to be so.

Is there any background mathematical question behind this or is this just a speculation you have?

[PTTG??]

Just a speculation, really.

Another way you might put that, then, is:

X>Y
X-Y=Z
What is the smallest value of Z?

But WAIT!

According to this,
Z=0.000...1
Since we know that 0.999... = 1, does not:
1-Z= 0.999...
1-Z= 1
Z=0

Or, put more simply, 0.000...1 is not just almost, or not just approaches, but actually is equal to zero? And then must we assume that since the smallest possible difference between X and Y in X>Y is 0, that for X>Y, it's possible for X=Y? And thus, any number is larger and smaller than itself?

I need to go lay down.

[Angellus]

No, that is significance of numbers, for example, if you count euro's (or dollars) You won't go any further than 2 decimals after the dot, 3 if you're an energy or water supplier. The actual value on the other hand, stays as it is.

You would just say the minimum of Z roughly equals X in most cases.
1,00 actually means 1,00 +/- 0,005.

Another way you might put that, then, is:

X>Y
X-Y=Z
What is the smallest value of Z?

Y was larger then X, not?
If X<Y, then it cannot be that X=Y, in significance, yes, but it would be significant to state that you are higher, thus the .......1 becomes significant, at least in calculations.
After calculating it might just be possible that you end up with the same number due to significance, but it would not be the same number.

Whoa, I'm starting to get your drift I think...

[MagmaDeath]

The one hole in your theory is that .999... is not equal to one. They are separate numbers no matter how you look at it.With the parameters you outlined, this is what actually happens.
X>Y
X-Y=Z
So Z is .00000...1
But
.9999... is always .9999... and .000...1 is always .000...1 In pure math. So
1-Z is always .9999... not 1
Therefore Z is not equal to zero, and X does not equal Y.

[eerr]

Z can be any number Y could be.

Because, for any number Y could be, there is always a smaller number.
so if Y becomes a smaller number, then Z can be any number Y could be.

Domain is no place for infinity!

[Angellus]

Z can be any number Y could be.

Because, for any number Y could be, there is always a smaller number.
so if Y becomes a smaller number, then Z can be any number Y could be.

Domain is no place for infinity!

I really felt like your avatar there XD

[eerr]

Z can be any number Y could be.

Because, for any number Y could be, there is always a smaller number.
so if Y becomes a smaller number, then Z can be any number Y could be.

Domain is no place for infinity!

I really felt like your avatar there XD

You should see what I had to cut out to keep that simple!

[Angellus]

Z can be any number Y could be.

Because, for any number Y could be, there is always a smaller number.
so if Y becomes a smaller number, then Z can be any number Y could be.

Domain is no place for infinity!

I really felt like your avatar there XD

You should see what I had to cut out to keep that simple!

It is due to the shortness yet fullness of the bit

[PTTG??]

The one hole in your theory is that .999... is not equal to one.

I'm afraid you're wrong there. For instance:
A/B = C
C*B = A
Right? So therefore:
1/3 = 0.333...
0.333 * 3 = 0.999...
0.999 must equal 1.
Wikipedia can't be wrong (for very long, anyway)

Anyway, Z in my earlier statements means 0.000...1 That is, an infinite number of zeros, followed (or, depending on how you read, lead) by a 1. In other notation, you might put it as (1/infinity). I'm iffy on transcendental and multiple infinities. My judgment is that Even if Y is 0.000...1, there isn't any 0.000...01 (that would also be written as 0.000...1, and would have the same value), for instance. The only lower number is 0.000...0, or 0.

[bjlong]

The problem with this logic is that .000...1=0, for the same reason .999...=1. Therefore, saying that the number 1.000...1>1 makes no sense. Same thing for 1/inf.

Wondering what the smallest number of Y is isn't a good question--there's an infinity of numbers between any two numbers.

[Angellus]

The one hole in your theory is that .999... is not equal to one.

I'm afraid you're wrong there. For instance:
A/B = C
C*B = A
Right? So therefore:
1/3 = 0.333...
0.333 * 3 = 0.999...
0.999 must equal 1.
Wikipedia can't be wrong (for very long, anyway)

Anyway, Z in my earlier statements means 0.000...1 That is, an infinite number of zeros, followed (or, depending on how you read, lead) by a 1. In other notation, you might put it as (1/infinity). I'm iffy on transcendental and multiple infinities. My judgment is that Even if Y is 0.000...1, there isn't any 0.000...01 (that would also be written as 0.000...1, and would have the same value), for instance. The only lower number is 0.000...0, or 0.

Damn that's a mean one!

[Jreengus]

1+(1/inf.)

FYI you should never use infinity as a number, that's horrible horrible mathematics as it doesn't act like other numbers.

The problem with this logic is that .000...1=0, for the same reason .999...=1. Therefore, saying that the number 1.000...1>1 makes no sense. Same thing for 1/inf.

Wondering what the smallest number of Y is isn't a good question--there's an infinity of numbers between any two numbers.

Yup you just say Y is arbitrarily close to 1 and leave it at that. For the same reason Z is arbitrarily close to 1

[PTTG??]

The problem with this logic is that .000...1=0, for the same reason .999...=1. Therefore, saying that the number 1.000...1>1 makes no sense. Same thing for 1/inf.

Wondering what the smallest number of Y is isn't a good question--there's an infinity of numbers between any two numbers.

I think you've hit it on the head, there. The smallest possible Z is NOT 0.000...1, because that IS 0. So, Z is greater than 0.000...1. How much greater? precisely the smallest amount greater than something that something can be without being the same... which is exactly the same as what we've been trying to solve.

In other words, we've discovered that the smallest possible value of Z is the smallest possible value of Z.

Hm...

[eerr]

The problem with infinity is that so many operations are undefined.
Also, people use it without regards as to where to came from!

what spontaneously caused "a 1/infinity" in your system?

I mean, seriously!
Also, there were about 10 examples of 0.999...9=1 on wikipedia,
as well as 3 examples of 0.999 not equal to 1.
So thats an awfully poor way to resolve this dispute!

If you stop using infinity the problem might loose this "infinite difficulty"
: P