obsrvr524
(obsrvr524)
January 13, 2020, 9:51pm
1458
Neither of those claims make any sense to me. So you haven’t proven anything to me. Why would your first claim be true?
Silhouette:
Saying there’s always a smaller gap, therefore there always is “a” gap that never fully vanishes, is no different from saying there’s never any point at which the gap can be said to come into existence.
That one doesn’t make any sense either.
Ecmandu
(Ecmandu)
January 13, 2020, 9:53pm
1459
I suppose what you want to say is: no gap between numbers = no difference between numbers = equal numbers. If that’s what you’re trying to say, then I agree.
That’s not the point of our disagreement. What we’re disputing is your claim that there is no gap between (0.\dot01) and (0).
Saying there’s always a smaller gap, therefore there always is “a” gap that never fully vanishes, is no different from saying there’s never any point at which the gap can be said to come into existence.
This is the problematic statement. It’s a non-sequitir.
A non-existent gap would be a gap that has zero size. The size of an infinitely small gap is greater than zero – by definition. No partial product of (\frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \cdots) is equal to (0). Note that this is different from (0 \times 0 \times 0 \times \cdots) where every partial product is equal to (0). Both are infinite, never-ending, products but one evaluates to a finite number that is (0) (is equal to it) whereas the other doesn’t evaluate to any finite number and is provably greater than (0).
I’ll argue Silhouette for silhouette!
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!
obsrvr524
(obsrvr524)
January 13, 2020, 9:59pm
1460
Silhouette:
“They” have a proof that if (0\times{n}=0), “n” can be any number you want since all numbers multiplied by zero equal zero. Therefore dividing both sides by 0 to get (\frac0{0}) it’s not (\infty) that this equals, but “undefined”.
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.
Ecmandu
(Ecmandu)
January 13, 2020, 10:04pm
1461
obsrvr524:
Silhouette:
“They” have a proof that if (0\times{n}=0), “n” can be any number you want since all numbers multiplied by zero equal zero. Therefore dividing both sides by 0 to get (\frac0{0}) it’s not (\infty) that this equals, but “undefined”.
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
(obsrvr524)
January 13, 2020, 10:08pm
1462
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
(Ecmandu)
January 13, 2020, 10:10pm
1463
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.
obsrvr524
(obsrvr524)
January 13, 2020, 10:12pm
1464
I wasn’t using any operators. I was talking about the static situation of an already infinite string.
Ecmandu
(Ecmandu)
January 13, 2020, 10:15pm
1465
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!
obsrvr524
(obsrvr524)
January 13, 2020, 10:20pm
1466
That might be so but I wasn’t multiplying anything. People who tried that as a proof have that issue, not me.
Ecmandu
(Ecmandu)
January 13, 2020, 10:25pm
1467
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
(obsrvr524)
January 13, 2020, 10:35pm
1468
No I don’t. “0.333…” is not a quantized number, a “quantity”. But 1/3 is a quantity.
I agree that math operators do not work on non-quantity items (anything ending with “…”).
Ecmandu
(Ecmandu)
January 13, 2020, 10:45pm
1469
So, obsrvr,
So, This is an interesting theory of numbers!
9/3 = 3
10/3 = 3
obsrvr524
(obsrvr524)
January 13, 2020, 11:20pm
1470
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?
obsrvr524
(obsrvr524)
January 14, 2020, 12:07am
1472
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?
obsrvr524
(obsrvr524)
January 14, 2020, 12:12am
1473
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
Ecmandu
(Ecmandu)
January 14, 2020, 12:27am
1474
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
(0.000\dotso1) represents (\frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \cdots).
This infinite product never attains (0).
Ecmandu
(Ecmandu)
January 14, 2020, 1:12am
1476
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?