SuSa
Banned via Administration
Except I said that from the start Omni. GG.
Last time I make a blog at 1am either. <_< This was a disaster.
Last time I make a blog at 1am either. <_< This was a disaster.
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0.999... = 1
- Thread starter SuSa
- Start date
10 is closer to infinity than 3. That is how you can approach infinity. Each time you add a positive number to another number, you get closer to infinity. We can model this effect and look for a pattern. That pattern converges at a single value. In this case that value is one.
It is why we can say if x is infinity than x/((x+1)^2) is REALLY small even though x can't really be defined by numbers. All infinities are not equal. y=(X+c)^2 approaches infinity MUCH faster than y=x+c c is any constant.
It is why we can say if x is infinity than x/((x+1)^2) is REALLY small even though x can't really be defined by numbers. All infinities are not equal. y=(X+c)^2 approaches infinity MUCH faster than y=x+c c is any constant.
SuSa
Banned via Administration
False, because infinity is not a number. Nor is it necessarily positive, nor is it a whole number.
This is again giving a concept a speed. You can approach the speed of light - because the speed of light is a fixed speed. You can always move faster. Simply by walking, I have approached the speed of light.
Infinity is a concept. It's never stopping. Nor is it moving at a rate, you cannot define this rate. Just because you're moving faster in comparison to another does not mean that either are approaching infinity. The reason I used a real life analogy to display infinity is because I feel it's the only way most people can grasp this concept. Let me try a math one.
I'm moving at x.
You're moving at x^2
We are trying to approach something, let's say it's moving speed y.
In order to approach y, x > y must be true.
In order for you to be approaching faster, x < y but x^2 > y
However you cannot define infinity's speed, therefore it is impossible to say if you approaching it at all. You are moving faster than me, but neither of us are approaching.
This is again giving a concept a speed. You can approach the speed of light - because the speed of light is a fixed speed. You can always move faster. Simply by walking, I have approached the speed of light.
Infinity is a concept. It's never stopping. Nor is it moving at a rate, you cannot define this rate. Just because you're moving faster in comparison to another does not mean that either are approaching infinity. The reason I used a real life analogy to display infinity is because I feel it's the only way most people can grasp this concept. Let me try a math one.
I'm moving at x.
You're moving at x^2
We are trying to approach something, let's say it's moving speed y.
In order to approach y, x > y must be true.
In order for you to be approaching faster, x < y but x^2 > y
However you cannot define infinity's speed, therefore it is impossible to say if you approaching it at all. You are moving faster than me, but neither of us are approaching.
I feel like you are just trying to be difficult.
You are taking a mathematical concept and applying philosophy to it.
Infinity IS a quantity. It just can't be defined, because nothing can be greater than it. There is also negative infinity and infinitely small. When working with infinities, you observe patterns and make conclusions based on their convergence. It is legitimate Science. Although the quantity of infinity in Math cannot be defined. It CAN be predicted.Dictionary said:
You are taking a mathematical concept and applying philosophy to it.
D
Deleted member
Guest
quantity =/= number
infinity does not actually lie on the real line, it is merely the conceptual end of it.
infinity does not actually lie on the real line, it is merely the conceptual end of it.
I mean i can use 4th grader terms to define limits but it doesn't change the fact that as numbers get VERY BIG certain mathematical functions approach certain numbers. The bigger the inputs get, the closer it gets to said limit. The number can get as close as you want to the limit without reaching it, but it will never surpass the limit. So the limit of that function as numbers get larger than you or anyone could ever count is a single definable number.
f(n) = .9 + .09 + .009 + .... + .(n 0's)9
the bigger n gets the closer f(n) gets to 1. It can never be greater than one but it gets closer than any number you can define. If there is no definable number between f(n) as n gets uncountably big and 1, than f(n) goes to 1.
f(n) = .9 + .09 + .009 + .... + .(n 0's)9
the bigger n gets the closer f(n) gets to 1. It can never be greater than one but it gets closer than any number you can define. If there is no definable number between f(n) as n gets uncountably big and 1, than f(n) goes to 1.
Palpi
Smash Hero
Go from point a to point b which is 10 feet by going half of the remaining distance each step.
D
Deleted member
Guest
I see a Zeno reference.
SuSa
Banned via Administration
Such precision is not humanly possible.
LordoftheMorning
Smash Champion
I'm really surprised this has merited such lengthy discussion. Here's how it breaks down.
I'd first like to point out that between any two real numbers is another real number. That's a mathematical fact.
Now let's apply this to the two numbers 0.999... (repeating) and 1.
Is there a number that you can place INBETWEEN .999... and 1? No. Because the nines literally go on indefinitely.
Because there is no real number that exists between .999... and 1, we can, therefore, conclude that .999... and 1 are the exact same number, which can be stated "1=0.999..."
It doesn't really matter how we express it. Math is abstract, so the limits of our ability to express infinite repeating number is irrelevant.
I'd first like to point out that between any two real numbers is another real number. That's a mathematical fact.
Now let's apply this to the two numbers 0.999... (repeating) and 1.
Is there a number that you can place INBETWEEN .999... and 1? No. Because the nines literally go on indefinitely.
Because there is no real number that exists between .999... and 1, we can, therefore, conclude that .999... and 1 are the exact same number, which can be stated "1=0.999..."
It doesn't really matter how we express it. Math is abstract, so the limits of our ability to express infinite repeating number is irrelevant.
D
Deleted member
Guest
you're kinda late with that "rule" (It's a definition), I already mentioned that on the previous page.
LordoftheMorning
Smash Champion
Why are you correcting me if I'm correct? -.-
D
Deleted member
Guest
>Implying I'm incorrect
A Pimp Named Slickback
Smash Lord
SuSa was just being stubborn.
that's why the thread lasted this long
that's why the thread lasted this long
SuSa isnt being stubborn, you're just really easily trolled lmao
A Pimp Named Slickback
Smash Lord
nah .
lucassassin
Smash Cadet
did anyone else notice that if x=0.9 then 10x=9.0 not 9.9 this makes the rest of the proof invalid.
please correct me if i'm wrong
Pretty sure he was using ... as the suggestion that the 9 went on forever.
So what he was saying was:
x = 0.999
10x = 9.999
10x - x = 9
9x = 9
x = 1
someone correct me if I'm wrong lol. I hate math.
Ninja'd awesomeface.png
Seikend
Smash Journeyman
- Joined
- Apr 16, 2007
- Messages
- 415
The dots imply that it's an infinite sequence.
So it's not x = 0.9
but x =0.9999999999999 etc.
It's just a mathematical shorthand.
Edit:Ninja'd frownyface.jpg
Jonkku
Lacks pick-up lines.
- Joined
- Jun 23, 2006
- Messages
- 5,842
Don't you mean 90 degrees each?
- Joined
- May 3, 2009
- Messages
- 7,190
I agree with the OP. The infinitely repeating decimals you get from dividing 1 by 3 only serve a practical purpose.
Yeah, I hate math too, but the reason I decided to take two classes of it this year is because I think it'll look good on my transcript. Y/N?
Oh yeah it'll look good.
A lot can be said for someone who has the patience and/or ability to do well at maths.
I only had the latter lol, and ability doesn't give you free knowledge unfortunately. ;__;
INSANE CARZY GUY
Banned via Warnings
I like this thread but only problem this .9999999999....=1 is if we took both numbers and timed them by a number equally as long 1 and .99999999999999... would we get the same answer because what's it's timed by is just as long so wouldn't it have a change somewhere? 99999999999999999.99999999999999.... x .9999999999999...........= 1 times the other inf. long number.
that and wouldn't that mean the very last place of numbers don't matter if substracted or plus 1? if so wouldn't that mean there's a point where the number value doesn't matter and there are in fact 2 copies of the same number but the problems are if we infly added .999... together it'd go to .9999.....89 and if you keep adding them they'd slowly go farther away from 1x whatever
I think .999999999........ = 1 is both right, wrong and our number system is broken.
I like how this thread/idea proves how we can't even count right and how little we know the reason is for the truth and to learn. what's to learn? If you never know you wasted your own time.
that and wouldn't that mean the very last place of numbers don't matter if substracted or plus 1? if so wouldn't that mean there's a point where the number value doesn't matter and there are in fact 2 copies of the same number but the problems are if we infly added .999... together it'd go to .9999.....89 and if you keep adding them they'd slowly go farther away from 1x whatever
I think .999999999........ = 1 is both right, wrong and our number system is broken.
I like how this thread/idea proves how we can't even count right and how little we know the reason is for the truth and to learn. what's to learn? If you never know you wasted your own time.
D
Deleted member
Guest
ICG, you make the mistake of assuming that 0.9...+0.9... =/= 1.9... but has and end somewhere (which in that case will bring in an 8 yes).
please either disprove any of the given proofs, provide and actual mathematical proof that something goes wrong if we "assume" that 0.9...=1 or don't reply.
please either disprove any of the given proofs, provide and actual mathematical proof that something goes wrong if we "assume" that 0.9...=1 or don't reply.
INSANE CARZY GUY
Banned via Warnings
no I'm saying at the end of the .99999999...s if you added them they'd have an 8 and would slowly drop. YES it does equal 1 but if times a inf. high high with as many numbers as 9s it has it would fall to like .99999... 89 ..
also seeing how this is right doesn't this make it so we have 2 of the same number for each other number?
.333333.... + .3333333..... last number a 6 even if there is no last number. i'm out
also seeing how this is right doesn't this make it so we have 2 of the same number for each other number?
.333333.... + .3333333..... last number a 6 even if there is no last number. i'm out
D
Deleted member
Guest
there is NO end. therefore there would not be an 8.
Fried Ice Cream
Smash Ace
Please don't be a **** to anyone who takes interest in an open blog but hasn't taken maths on a higher level.
Anyone has the privelege to post in Blogs.
A Pimp Named Slickback
Smash Lord
privilege to post doesn't mean you are immune from being corrected when wrong
Fried Ice Cream
Smash Ace
Still, telling someone to not reply to a blog if you don't know the subject completely isn't that way to go, even though it's not a smart thing to do.
D
Deleted member
Guest
but completely disregarding posted proofs isn't the way to go either. I know I sounded harsh but most things have been said by now and then coming in and saying "I think the number system is broken" just made me go >_> tbh
A Pimp Named Slickback
Smash Lord
that's funny
because that's what this entire blog is about
because that's what this entire blog is about
D
Deleted member
Guest
I meant without much else than intuition behind it.
SuSa
Banned via Administration
If I can't add/subtract 0.999... because it never ends (therefore if I did add something to it, when would it be added?)
How is it okay to multiply it by 10? My thought process (which is 99.99% likely to be wrong :D) has always taken multiplication as addition.
10 x 2 = 10 + 10 or 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2
5 x 4 = 5 + 5 + 5 + 5 or 4 + 4 + 4 + 4 + 4
Therefore...
x = 0.999...
10x = 9.999...0 ||| Invalid. Cannot compute.
1) If you can add nothing to infinity. How can you add itself? Let alone 10 times?
You have to remember what multiplication hints at.
It's addition.
How is it okay to multiply it by 10? My thought process (which is 99.99% likely to be wrong :D) has always taken multiplication as addition.
10 x 2 = 10 + 10 or 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2
5 x 4 = 5 + 5 + 5 + 5 or 4 + 4 + 4 + 4 + 4
Therefore...
x = 0.999...
10x = 9.999...0 ||| Invalid. Cannot compute.
1) If you can add nothing to infinity. How can you add itself? Let alone 10 times?
You have to remember what multiplication hints at.
It's addition.
Seikend
Smash Journeyman
- Joined
- Apr 16, 2007
- Messages
- 415
You can add 0.99.....If I can't add/subtract 0.999... because it never ends (therefore if I did add something to it, when would it be added?)
How is it okay to multiply it by 10? My thought process (which is 99.99% likely to be wrong :D) has always taken multiplication as addition.
10 x 2 = 10 + 10 or 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2
5 x 4 = 5 + 5 + 5 + 5 or 4 + 4 + 4 + 4 + 4
Therefore...
x = 0.999...
10x = 9.999...0 ||| Invalid. Cannot compute.
1) If you can add nothing to infinity. How can you add itself? Let alone 10 times?
You have to remember what multiplication hints at.
It's addition.
But you can't say that the last value of 0.99.... + 0.99.... is an 8. There is no last value.
Jim Morrison
Smash Authority
Infinity doesn't even make sense.
Good thing we never have to work with it.
Good thing we never have to work with it.
SuSa
Banned via Administration
I'm genuinely confused. =|
I blame being taught that 10 * x = shift over everything 1 spot to the left and add a 0.
=[
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Also quick personal message to EVERYONE who has asked for how far I've gotten in math. The answer is Algebra... self-taught Geometry, Trig, parts of Alg. 2 (which I'm taking currently for Independant Study.. meaning I'm teaching myself from the book), and it's always been my strongest subject... but moving around as much as I do I've never actually been able to study it as most people get to properly... so if you can put up with my ignorance and just point things out - if it's not 2-3am I'll likely understand it. I'm not a ******* I'm just really slow when I'm tired. So if you can try to stay away from insulting my intelligence that'd be nice. Considering, not having taken a formal math class in 3 years and I still can't even solve radicals. =\
Thank you,
SuSa.
I blame being taught that 10 * x = shift over everything 1 spot to the left and add a 0.
=[
----------------------------------------------
Also quick personal message to EVERYONE who has asked for how far I've gotten in math. The answer is Algebra... self-taught Geometry, Trig, parts of Alg. 2 (which I'm taking currently for Independant Study.. meaning I'm teaching myself from the book), and it's always been my strongest subject... but moving around as much as I do I've never actually been able to study it as most people get to properly... so if you can put up with my ignorance and just point things out - if it's not 2-3am I'll likely understand it. I'm not a ******* I'm just really slow when I'm tired. So if you can try to stay away from insulting my intelligence that'd be nice. Considering, not having taken a formal math class in 3 years and I still can't even solve radicals. =\
Thank you,
SuSa.
Seikend
Smash Journeyman
- Joined
- Apr 16, 2007
- Messages
- 415
This won't be a perfect explanation, and it might break one of your rules, but I hope you'll see what's happening rather than try to be dfficult.
Say you want to add 0.999.... to 0.999....
With normal rules, you add the 0 and the 0. You get 0
Then you move to the next decimal position, which is the first 9. You add 9 + 9 to get 1.8.
You now have 1.8
Once again, next decimal position, and once again, it's another set of 9s. You add 9+9 to get 1.8
You now have 1.98
Once again, next decimal position, once again, it's another set of 9s. You add 9+9 to get 1.8
You now have 1.998
Now by the definition of infinite, it goes on forever right? So we have an infinite sequence of 9+9s. By adding this to the running total, we gain a 9 everytime. Therefore, we get an infinite sequence of 9s, or 1.99999....
Likewise for multiply by 10. If you follow it through each step from every decimal position.
I'm sure there's a better and more mathematical way to explain it using sets or whatever, but I was never fantastic at maths. But you can at least understand how it works?
Say you want to add 0.999.... to 0.999....
With normal rules, you add the 0 and the 0. You get 0
Then you move to the next decimal position, which is the first 9. You add 9 + 9 to get 1.8.
You now have 1.8
Once again, next decimal position, and once again, it's another set of 9s. You add 9+9 to get 1.8
You now have 1.98
Once again, next decimal position, once again, it's another set of 9s. You add 9+9 to get 1.8
You now have 1.998
Now by the definition of infinite, it goes on forever right? So we have an infinite sequence of 9+9s. By adding this to the running total, we gain a 9 everytime. Therefore, we get an infinite sequence of 9s, or 1.99999....
Likewise for multiply by 10. If you follow it through each step from every decimal position.
I'm sure there's a better and more mathematical way to explain it using sets or whatever, but I was never fantastic at maths. But you can at least understand how it works?
You need a calculus class. It would definitely clear this stuff up a bit.
SuSa
Banned via Administration
Sadly, depending on the classes offered at the colleges I'm going to, I'm unlikely to receive said class.
Really sucks getting shafted by a horrible education system (Hey everywhere! Teach different **** at different times!
) If I didn't move in my Alg. 2 class which was doing Alg. 1 review (first 2 months of the class? Come on.. a few days of review is fine...) to an Alg. 2 class in the middle of solving radicals (a month of this, all going over my head because I never got around to getting tutoring from my teacher. Too busy trying to get A's in my other classes), moving to an independent study - where I didn't take a math class for a full on year; and now I'm at a new independent study where I start my math class the week after next...
All because my first class had to do 2 months of review because people didn't understand basic ****ing concepts. (AKA: Things they learned already)
I mean... I could understand if all that information was new.... but do we really need to spend a week or two solving basic algebraic problems like 9x + 4 = 40? Like... REALLY now?
I'll see if there's any possible way. I'm a bit ahead on credits and I'm not sure what math classes my independent study has to offer. Even if it's self-taught out of a book. That's x10 better than nothing at all.
@Seikend
Understand how it works. Yay for simple explanations.
//should request a thread lock... but meh