But the absolute numerical fact is 0.9 recurring is not 1.
I would non-sarcastically love to see your proof of that. If you can provide me a non-fallacious proof that .9999... ≠ 1, I will go down stairs, set my webcam to stream and eat my hat live.
I would non-sarcastically love to see your proof of that. If you can provide me a non-fallacious proof that .9999... ≠ 1, I will go down stairs, set my webcam to stream and eat my hat live.
Thats pretty easy to prove, just look here, and tell me if they look the same.
I would non-sarcastically love to see your proof of that. If you can provide me a non-fallacious proof that .9999... ≠ 1, I will go down stairs, set my webcam to stream and eat my hat live.
0.9 recurring is never 1 - there is always an infinitely small gap.
It may be such a small gap that for every human use of numbers they are the same, but the fact is there is a gap, and therefore 0.9 recurring is not 1.
Except that's not a proof, that's taking two expressible numbers that do in fact happen to be different and asserting that latter of them is an equivalent expression of .9999...
Σ 9 * (.1^-n) where n=1->1904 is not the same as Σ 9 * (.1^-n) where n=1->∞
And while we're on the topic of false equivalencies your analogy with pi is flawed as pi, unlike .9999 is neither a rational number nor a repeating decimal.
0.9 recurring is never 1 - there is always an infinitely small gap.
It may be such a small gap that for every human use of numbers they are the same, but the fact is there is a gap, and therefore 0.9 recurring is not 1.
For that "infinitely small gap" you posit there has to be an expressible value for it. You assert that expression cannot be 0, otherwise the the two numbers would in fact be the same. Might I offer you a proof by contradiction?
Let .9999... ≤ 1
Assume .9999... ≠ 1
Then .9999... < 1
Therefore there must be some positive number N such that .9999 + N = 1 (I think we can agree here since it's your own assertion)
However for any positive value for N, .9999... + N > 1
In mathematics if a line of reasoning is correct and the conclusion arrived at is wrong then it must follow that the initial assumption is incorrect.
Except that's not a proof, that's taking two expressible numbers that do in fact happen to be different and asserting that latter of them is an equivalent expression of .9999...
Σ 9 * (.1^-n) where n=1->1904 is not the same as Σ 9 * (.1^-n) where n=1->∞
And while we're on the topic of false equivalencies your analogy with pi is flawed as pi, unlike .9999 is neither a rational number nor a repeating decimal.
It's called common ground...
Not everyone understands the equations, but most people can compare two things and determine if they look alike.
IMO going nuts with as complicated math equations as possible mostly only serves to make other people feel dumb, just because the user does not understand them.
That is not the case, it's just different cases of understandable-intelligence, and can not be used to measure total-intelligence.
Don't look silly... Don't call it the "Z-Store/Zen Store"...
Not everyone understands the equations, but most people can compare two things and determine if they look alike.
IMO going nuts with as complicated math equations as possible mostly only serves to make other people feel dumb, just because the user does not understand them.
That is not the case, it's just different cases of understandable-intelligence, and can not be used to measure total-intelligence.
I thought I tried to be diplomatic when I explained right off the bat in my first post that I was NOT intending to be a pedant and that it was simply a personal pet peeve, and again one post later. The only reason I got down to fussing over increasingly small details is it was the only clear way of explaining myself more precisely.
For that "infinitely small gap" you posit there has to be an expressible value for it. You assert that expression cannot be 0, otherwise the the two numbers would in fact be the same. Might I offer you a proof by contradiction?
Let .9999... ≤ 1
Assume .9999... ≠ 1
Then .9999... < 1
Therefore there must be some positive number N such that .9999 + N = 1 (I think we can agree here since it's your own assertion)
However for any positive value for N, .9999... + N > 1
In mathematics if a line of reasoning is correct and the conclusion arrived at is wrong then it must follow that the initial assumption is incorrect.
Nope, there is a positive value of N where 9.9999... + N = 1, and an infinite number of values of N where 0.9999... + N <1.
I'm not picking on you, atomictiki. Please understand what's being said here.
In a real world context, you wouldn't have this argument at the Apple Store about the newest products. You wouldn't get answers like this at a car dealership, etc.
And Cryptic/PWE certainly isn't going to answer this, imho.
I know you're not picking on me, because the real world car/iphone arguments are some of the weakest and most ludicrous I've seen about this issue.
Roads don't increase in level every year and we don't live in a Mad Max world (yet!) so there's no reason to "upgrade" your car beyond sheer vanity every year. Same with an iPhone, although there you are dealing with a lot of inherent planned obsolescence from the get go - but Apple worshippers expect it (and in many cases demand it).
Now, I do agree that as customers we need to see Cryptic's road map so we can make informed decisions about their products, which was the point of this thread.
till the next level cap increase. this is sop for mmos. level is x and this is end game... next expansion and now level cap is y and your level x uber loot is not so uber anymore. get over it or play a standalone game.
Yes, for 99% of all MMOs your end gear comes from crafting (like GW2) or endgame raids (WOW).
You don't buy your Breastplate of Radiant Awesomeness +10 for $25 every expansion in Rift.
It's a loot drop or you craft it from loot drops.
The major sticking point is that ships are not gear. They're character avatars. The phaser banks, shields, engines, etc. is the gear that is meant to be obsolete and no one is upset about it.
I am not about to write out a really obvious infinite number just to win an argument on the internet.
I love how this got threadjacked into a math thread. The point isvarna is trying to make with proofs is that the number you'd have to add to 0.9999... in order for it to equal 1 does not exist.
We all agree that we're looking for a number N to satisfy this equation:
0.999... + N = 1
Any finite value of N would lead to a sum greater than 1.
If N = 0.000..., you'll still not equal 1.
If N = 0.000...001 (basically a mythical number that is infinite 0s somehow followed by a 1) you'll get a number greater than 1.
Therefore, since there are no numbers between 0.999... and 1, they are the same number.
Also, no one should feel dumb for not understanding all this. It's all theoretical and academic, since in the real world (as an engineer or programmer, for example) you would almost never have to deal with actual repeating numbers in this manner.
Comments
I would non-sarcastically love to see your proof of that. If you can provide me a non-fallacious proof that .9999... ≠ 1, I will go down stairs, set my webcam to stream and eat my hat live.
Thats pretty easy to prove, just look here, and tell me if they look the same.
1
0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
and that one is not even the complete.
For the same reasons, Pi is Pi, and not 3.14
0.9 recurring is never 1 - there is always an infinitely small gap.
It may be such a small gap that for every human use of numbers they are the same, but the fact is there is a gap, and therefore 0.9 recurring is not 1.
Except that's not a proof, that's taking two expressible numbers that do in fact happen to be different and asserting that latter of them is an equivalent expression of .9999...
Σ 9 * (.1^-n) where n=1->1904 is not the same as Σ 9 * (.1^-n) where n=1->∞
And while we're on the topic of false equivalencies your analogy with pi is flawed as pi, unlike .9999 is neither a rational number nor a repeating decimal.
EDIT to avoid double post
For that "infinitely small gap" you posit there has to be an expressible value for it. You assert that expression cannot be 0, otherwise the the two numbers would in fact be the same. Might I offer you a proof by contradiction?
Let .9999... ≤ 1
Assume .9999... ≠ 1
Then .9999... < 1
Therefore there must be some positive number N such that .9999 + N = 1 (I think we can agree here since it's your own assertion)
However for any positive value for N, .9999... + N > 1
In mathematics if a line of reasoning is correct and the conclusion arrived at is wrong then it must follow that the initial assumption is incorrect.
It's called common ground...
Not everyone understands the equations, but most people can compare two things and determine if they look alike.
IMO going nuts with as complicated math equations as possible mostly only serves to make other people feel dumb, just because the user does not understand them.
That is not the case, it's just different cases of understandable-intelligence, and can not be used to measure total-intelligence.
I thought I tried to be diplomatic when I explained right off the bat in my first post that I was NOT intending to be a pedant and that it was simply a personal pet peeve, and again one post later. The only reason I got down to fussing over increasingly small details is it was the only clear way of explaining myself more precisely.
Nope, there is a positive value of N where 9.9999... + N = 1, and an infinite number of values of N where 0.9999... + N <1.
Still waiting on what that value is.
Edit: Any potential hat-eating will have to wait until tomorrow. I will check up on this thread in the morning.
I am not about to write out a really obvious infinite number just to win an argument on the internet.
I know you're not picking on me, because the real world car/iphone arguments are some of the weakest and most ludicrous I've seen about this issue.
Roads don't increase in level every year and we don't live in a Mad Max world (yet!) so there's no reason to "upgrade" your car beyond sheer vanity every year. Same with an iPhone, although there you are dealing with a lot of inherent planned obsolescence from the get go - but Apple worshippers expect it (and in many cases demand it).
Now, I do agree that as customers we need to see Cryptic's road map so we can make informed decisions about their products, which was the point of this thread.
Yes, for 99% of all MMOs your end gear comes from crafting (like GW2) or endgame raids (WOW).
You don't buy your Breastplate of Radiant Awesomeness +10 for $25 every expansion in Rift.
It's a loot drop or you craft it from loot drops.
The major sticking point is that ships are not gear. They're character avatars. The phaser banks, shields, engines, etc. is the gear that is meant to be obsolete and no one is upset about it.
I love how this got threadjacked into a math thread. The point isvarna is trying to make with proofs is that the number you'd have to add to 0.9999... in order for it to equal 1 does not exist.
We all agree that we're looking for a number N to satisfy this equation:
0.999... + N = 1
Any finite value of N would lead to a sum greater than 1.
If N = 0.000..., you'll still not equal 1.
If N = 0.000...001 (basically a mythical number that is infinite 0s somehow followed by a 1) you'll get a number greater than 1.
Therefore, since there are no numbers between 0.999... and 1, they are the same number.
Also, no one should feel dumb for not understanding all this. It's all theoretical and academic, since in the real world (as an engineer or programmer, for example) you would almost never have to deal with actual repeating numbers in this manner.