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.
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.
I don’t understand.
It’s means that 1/10th MOVES for EVERY 9 instead of the 1 never occurring (the “the end”)