Except that ∞, by definition is NOT a number (“n”).
So the “proof” using n/o is invalid.
So you are saying that you never get to the end??
And that would mean that there is always a “9”, never a “0” in 0.999…, wouldn’t it.
Except that ∞, by definition is NOT a number (“n”).
So the “proof” using n/o is invalid.
So you are saying that you never get to the end??
And that would mean that there is always a “9”, never a “0” in 0.999…, wouldn’t it.
Absolutely. But that’s not my focus right now, I’m debating Magnus on orders of infinity, that’s my focus.
I’ll get to Silhouette later.
obsrvr524:And that would mean that there is always a “9”, never a “0” in 0.999…, wouldn’t it.
Absolutely. But that’s not my focus right now, I’m debating Magnus on orders of infinity, that’s my focus.
So if it never has a zero at the end, because it doesn’t have an end, then it cannot be equal to 1.000…, which has zero throughout.
Ecmandu: obsrvr524:And that would mean that there is always a “9”, never a “0” in 0.999…, wouldn’t it.
Absolutely. But that’s not my focus right now, I’m debating Magnus on orders of infinity, that’s my focus.
So if it never has a zero at the end, because it doesn’t have an end, then it cannot be equal to 1.000…, which has zero throughout.
Yes. Correct. Actually, it can be best seen as a problem with operators … some think that problem makes an equality, and some (me) don’t.
obsrvr524:So if it never has a zero at the end, because it doesn’t have an end, then it cannot be equal to 1.000…, which has zero throughout.
Yes. Correct. Actually, it can be best seen as a problem with operators … some think that problem makes an equality, and some (me) don’t.
I wasn’t using any operators. I was talking about the static situation of an already infinite string.
Ecmandu: obsrvr524:So if it never has a zero at the end, because it doesn’t have an end, then it cannot be equal to 1.000…, which has zero throughout.
Yes. Correct. Actually, it can be best seen as a problem with operators … some think that problem makes an equality, and some (me) don’t.
I wasn’t using any operators. I was talking about the static situation of an already infinite string.
You don’t understand what you’re saying!
If 1/3 = 0.333…
And 0.333… *3 = 0.999… not 1/3!
That’s an operator problem!
If 1/3 = 0.333…
And 0.333… = 0.999…
That’s an operator problem!
That might be so but I wasn’t multiplying anything. People who tried that as a proof have that issue, not me.
Ecmandu:If 1/3 = 0.333…
And 0.333… = 0.999…
That’s an operator problem!
That might be so but I wasn’t multiplying anything. People who tried that as a proof have that issue, not me.
Do you agree that 1 whole number (1) divided by 3 equal 0.333… ?
Do you agree that 0.333… times 3 equals 0.999… ?
If all that is true, then operators don’t work. At least for base-1.
obsrvr524: Ecmandu:If 1/3 = 0.333…
And 0.333… = 0.999…
That’s an operator problem!
That might be so but I wasn’t multiplying anything. People who tried that as a proof have that issue, not me.
Do you agree that 1 whole number (1) divided by 3 equal 0.333… ?
Do you agree that 0.333… times 3 equals 0.999… ?
No I don’t. “0.333…” is not a quantized number, a “quantity”. But 1/3 is a quantity.
If all that is true, then operators don’t work. At least for base-1.
I agree that math operators do not work on non-quantity items (anything ending with “…”).
So, obsrvr,
So, This is an interesting theory of numbers!
9/3 = 3
10/3 = 3
I’m not seeing where you are getting that.
Why would 10/3 = 3?
Here’s a proof that (1 = 0).
((1 + 1 + 1 + \cdots) + 1 = 1 + 1 + 1 + \cdots)
Agree?
If the answer is yes, subtract (1 + 1 + 1 + \cdots) from both sides.
What do we get?
(1 = 0)
But if the answer is no, it appears to me that it follows that one of the two sides of the expression is greater than or less than the other – and that means that infinities come in different sizes.
Assuming that I’m wrong, can you help me understand what I’m doing wrong?
Let me see if I understand you.
You have an infinite line and under it you have a dot.
Then you subtract the infinite line away and are left with a dot.
And that confuses you?
And if that confuses you…
When you have 3 parallel lines and subtract 1 parallel line, how many are left?
2
If you then subtract another parallel line, how many are left?
0
2 - 1 = 0
I’m not seeing where you are getting that.
Why would 10/3 = 3?
I’m using shorthand before the expansion…
The expansion is .333…
The shorthand works just as well.
9/3 = 3
10/3 = 3
The latter is what Silhouette is arguing
The reason Silhouette sees no difference between .000…1 and zero is because the 1 in 0.000…1 is never arrived at. It’s ALWAYS zero!
(0.000\dotso1) represents (\frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \cdots).
This infinite product never attains (0).
Ecmandu:The reason Silhouette sees no difference between .000…1 and zero is because the 1 in 0.000…1 is never arrived at. It’s ALWAYS zero!
(0.000\dotso1) represents (\frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \cdots).
This infinite product never attains (0).
Actually, the only way it can NEVER equal a zero is if it adds 1/10th sequentially. Otherwise, it’s a zero.
Actually, the only way it can NEVER equal a zero is if it adds 1/10th sequentially. Otherwise, it’s a zero.
What does it mean to add 1/10th sequentially?
Ecmandu:Actually, the only way it can NEVER equal a zero is if it adds 1/10th sequentially. Otherwise, it’s a zero.
What does it mean to add 1/10th sequentially?
1/10th. STOP * 1/10th STOP. * 1/10th STOP etc…
I don’t understand.