Old 'fixed' bugs continue to re-appear

[alexzk]

I just did, by showing that we reach a contradiction if it isn't.

Not sure man, proper record would be

E = (1 + N) - (0.9999 + N)
then ur tricks with x10 work a bit different. I think u just messing "shifting point" which is */ by 10 and +-9, because 10 is base of "decimal system".
Try the same with 3* E for example.

 

[taniwha-qf]

I just did, by showing that we reach a contradiction if it isn't.

No, because you have a contradiction either way. What as happened is one contradiction was chosen as preferable over the other. Also, "1 = 0.9999..." is not true because it's missing an important bit: "lim".

 

[Brrokk]

No, because you have a contradiction either way. What as happened is one contradiction was chosen as preferable over the other. Also, "1 = 0.9999..." is not true because it's missing an important bit: "lim".

That's the three dots. Notation is hard in a text forum. People usually write 0.9 with a dot above the 9.

To summarise the proof in words, let E be the difference between 0.999... and 1. If E is zero everything is fine, but if it's positive we can deduce that it's less than itself, which is impossible. Since it's zero, the two numbers are equal.

No limiting processes or "infinitesimals" are involved in this proof, once we've already accepted the use of the three dots. It's just a property of numbers.

 

[alexzk]

That's the three dots. Notation is hard in a text forum. People usually write 0.9 with a dot above the 9.

To summarise the proof in words, let E be the difference between 0.999... and 1. If E is zero everything is fine, but if it's positive we can deduce that it's less than itself, which is impossible. Since it's zero, the two numbers are equal.

No limiting processes or "infinitesimals" are involved in this proof, once we've already accepted the use of the three dots. It's just a property of numbers.

... = period?
0.(9) then in () means "period" or "repeated"

E= 1 - 0.(9)

E != 0
lim(E) == 0

That is proper. Limit of E is zero. But not E itself.

 

[Crank Larson]

I just did, by showing that we reach a contradiction if it isn't.

No, you really didn't.

 

[taniwha-qf]

That's the three dots. Notation is hard in a text forum. People usually write 0.9 with a dot above the 9.

Yes, it is indeed three dots, which is often meant (in context) to mean that the preceding pattern is repeated.

 

[Brrokk]

... = period?
0.(9) then in () means "period" or "repeated"

E= 1 - 0.(9)

E != 0
lim(E) == 0

That is proper. Limit of E is zero. But not E itself.

Good grief.
No limiting processes were used in the proof.

 

[taniwha-qf]

Good grief.
No limiting processes were used in the proof.

Herein lies the problem.
When limiting processes are used (eg, lim n->inf, 1=9*sum(10^(-i), i=1 to n) (fancy way of saying 1=0.999...)), then I accept that 1 and 0.999... are equivalent. When limiting processes are not used, then I do not accept that they are equivalent, as 0.999... is infinitesimally smaller than 1 (and limits and infinitesimals are mutually exclusive).

 

[alexzk]

Yes, it is indeed three dots, which is often meant (in context) to mean that the preceding pattern is repeated.

I recall I was taught braces are used to show repeat of pattern like 0.(9) reads as zero-point-and-nine-in-period.

 

[Brrokk]

Herein lies the problem.
When limiting processes are used (eg, lim n->inf, 1=9*sum(10^(-i), i=1 to n) (fancy way of saying 1=0.999...)), then I accept that 1 and 0.999... are equivalent. When limiting processes are not used, then I do not accept that they are equivalent, as 0.999... is infinitesimally smaller than 1 (and limits and infinitesimals are mutually exclusive).

That's nonsense made of maths buzzwords. The real numbers don't include "infinitesimals". Two real numbers are either equal, or they have a non-zero difference.

 

[alexzk]

The real numbers don't include "infinitesimals".

You included it when added dots. You made E difference infinite small.

 

[taniwha-qf]

The real numbers don't include "infinitesimals".

Of course they don't. An infinitesimal is defined as being larger than 0, but smaller than any real non-zero number.

 

[Crimson Kaim]

I don't think it's worth fixing bugs at this point anymore if they keep re-appearing.
Seems like the project Elite: Dangerous has just become too large and cluttered. For each bug they fix, another one will take its place.
It appears that the quality of this project is too low to further support any kind of content addition/expansion.

 

[[PS4] Filthymick420]

No, because you have a contradiction either way. What as happened is one contradiction was chosen as preferable over the other. Also, "1 = 0.9999..." is not true because it's missing an important bit: "lim".

Reality is stranger than fiction because fiction has to at least be somewhat believable but reality has no such concern whether it makes sense or not

 

[taniwha-qf]

I don't think it's worth fixing bugs at this point anymore if they keep re-appearing.
Seems like the project Elite: Dangerous has just become too large and cluttered. For each bug they fix, another one will take its place.
It appears that the quality of this project is too low to further support any kind of content addition/expansion.

Oh, really now? Sure, if only bandaids are applied to bugs, then the bugs will reemerge, for sure. But no software is too large or complicated or even too cluttered to fix. Doesn't mean it will be affordable to do so, of course. However, "with enough eyes, all bugs are shallow" - Linus Torvalds.

 

[[PS4] Filthymick420]

Oh, really now? Sure, if only bandaids are applied to bugs, then the bugs will reemerge, for sure. But no software is too large or complicated or even too cluttered to fix. Doesn't mean it will be affordable to do so, of course. However, "with enough eyes, all bugs are shallow" - Linus Torvalds.

I think with fdev too hard to do just means having to work hard but that's not what they want to do

 

[Brrokk]

Of course they don't. An infinitesimal is defined as being larger than 0, but smaller than any real non-zero number.

So... if 1 and 0.999... both represent real numbers, the difference between them can't be one of those infinitesimals, because they aren't real numbers, and the difference of any two reals is another real. (The real numbers are closed under addition and every real has an additive inverse, so they are closed under subtraction as well).

The difference between those two numbers is therefore zero or non-zero.

If the difference is non-zero we reach the contradiction that it's smaller than itself, which is impossible for a real number.

There are only two possible conclusions:
1) 0.999... doesn't represent a real number.
2) It represents the same real number as 1.

Now, OK, the assertion that 0.999... represents a real number at all does depend on a limiting process. The real numbers are complete by definition: any convergent sequence of real numbers has a real limit. The sequence 0.9+0.09+0.009+... therefore has a real limit and that limit is what we mean by 0.999...

But once you accept that 0.999... is allowed to represent a real number, 1 is the only possible value it can have. Anything else will lead to a contradiction.

 

[taniwha-qf]

So... if 1 and 0.999... both represent real numbers, the difference between them can't be one of those infinitesimals, because they aren't real numbers, and the difference of any two reals is another real. (The real numbers are closed under addition and every real has an additive inverse, so they are closed under subtraction as well).

The difference between those two numbers is therefore zero or non-zero.

If the difference is non-zero we reach the contradiction that it's smaller than itself, which is impossible for a real number.

There are only two possible conclusions:
1) 0.999... doesn't represent a real number.
2) It represents the same real number as 1.

Now, OK, the assertion that 0.999... represents a real number at all does depend on a limiting process. The real numbers are complete by definition: any convergent sequence of real numbers has a real limit. The sequence 0.9+0.09+0.009+... therefore has a real limit and that limit is what we mean by 0.999...

But once you accept that 0.999... is allowed to represent a real number, 1 is the only possible values it can have. Anything else will lead to a contradiction.

And this is why limits were invented: because many mathematicians, for one reason or another, loathed infinitesimals but otherwise liked calculus (which was invented using infinitesimals). That is, limits were invented to avoid using infinitesimals.

 

[[PS4] Filthymick420]

So... if 1 and 0.999... both represent real numbers, the difference between them can't be one of those infinitesimals, because they aren't real numbers, and the difference of any two reals is another real. (The real numbers are closed under addition and every real has an additive inverse, so they are closed under subtraction as well).

The difference between those two numbers is therefore zero or non-zero.

If the difference is non-zero we reach the contradiction that it's smaller than itself, which is impossible for a real number.

There are only two possible conclusions:
1) 0.999... doesn't represent a real number.
2) It represents the same real number as 1.

Now, OK, the assertion that 0.999... represents a real number at all does depend on a limiting process. The real numbers are complete by definition: any convergent sequence of real numbers has a real limit. The sequence 0.9+0.09+0.009+... therefore has a real limit and that limit is what we mean by 0.999...

But once you accept that 0.999... is allowed to represent a real number, 1 is the only possible value it can have. Anything else will lead to a contradiction.

I feel like the US dollar is worth less than 1 of itself anymore these days

 

[Brrokk]

Maybe "proof by contradiction" seems a bit tricky for some. I've just read a clearer way:

Let x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1

If anyone wants to disagree, please do it by saying which step you disagree with.