RE: [split] 0.999... equals 1
October 9, 2009 at 4:32 pm
(This post was last modified: October 9, 2009 at 6:05 pm by Violet.)
Edit: I should note before i begin, that there are some people who do not think you can add or subtract an infinite (see
a few math teachers I know personally [and discussed the concept of infinity with] among them. Even the concept of infinity is not accepted by every mathematician as having the same definition or even in being possible... so how could all mathematicians be on board with the idea of .9^=1? Be aware that not everyone even agrees on infinity's concept in math... let alone on a specific concept. For the full context of the wikiquote: http://en.wikipedia.org/wiki/Infinity
I did read it... and I do not see how it is equal to 1.8. The point of the article is simply this: .9^ approaches 1... but never reaches it. It is http://en.wikipedia.org/wiki/Infintesimal far away from 1. Proof that infinitesimals exist (according to the wiki):
As you can see, infinitesimals exist as much as infinity... therefore my use of 0.0^1 (An infinitesimal number)... which you stated does not exist: essentially exists as much as .9^, which is an infinitesimal distance from one. Please do not insult me by suggesting I did not read the articles I used as evidence... esp. since I found them to be rather fascinating (therefore insulting what I find fascinating).
Also, I do not think wikipedia is an entirely trustable source... http://en.wikipedia.org/wiki/Wikipedia#Reliability
I'll start with the first one.
You removed the infinite from the equation when you subtracted it from itself. Essentially, you have cancelled out the effect of infinity. Your problem becomes this:
x=.9^
10x=9.9^
9.9^-.9^=9 (You will notice that you have cancelled out infinity in this step... therefore infinity is no longer a part of the equation.)
9(new x)=9
New x=1
Essentially... this 'proof' is invalid, because you have changed the value of X by canceling out the effect of infinity upon the number. As in, you are no longer proving that the first value of X (.9^)is equal to one... but that the new value (1) is. You changed the value of X when you canceled out part of the equation. Simply, 1-1=0... just as infinity - infinity=0. You negated its effect in your calculation, so that you could solve it without infinity's effect.
You accept that 2*10=20, 20-2=18, no? Then how come when we take 2*9, it is ≠ 18? Essentially, that is what is being done in this 'proof'. Registering different answers for 20-2 and 2*9 is a fallacy under finite circumstance... and is only (and according to some people, not even then) possible when eliminating an infinite or infinitesimal or other undefined number. For example, 10x2.2^-2.2^ would not be equal to 9x2.2^.
x=.9^
9x=8.9^1
8.9^1/9= .9^
Once you nullify the infinite part of x, then you are no longer proving .9^. You are proving a finite by canceling out the infinite. By doing so, you get a different answer for 10x-x, and for simply 9x. If this were a finite number to begin with: you would not get different results from those two normally equivalent expressions. I do not accept this 'proof' of an infinite equalling a finite... for it is only by the canceling of the infinite concept that the inequality can 'solved'.
Quote:1.79, 1.799, 1.7999,... We could observe that the numbers are "approaching" 1.8, the limit of the sequence.
I did read it... and I do not see how it is equal to 1.8. The point of the article is simply this: .9^ approaches 1... but never reaches it. It is http://en.wikipedia.org/wiki/Infintesimal far away from 1. Proof that infinitesimals exist (according to the wiki):
Also, I do not think wikipedia is an entirely trustable source... http://en.wikipedia.org/wiki/Wikipedia#Reliability
Quote:Do you not think that if this were some kind of disproof, the 0.999 page at Wikipedia would mention it? No. Instead it shows 2 elegant proofs (which I repeated here with the addition of another) of how 0.9... = 1.So yes, I think it is possible that a disproof might not be mentioned. I was not convinced by these pages of proofs, and so I will actively hunt down each one and disprove it. In previous posts, i just suggested that the notion of this inequality being equal was laughable... now I am giving evidence to back up my previous laughter.
I'll start with the first one.
Quote:No it doesn't. 1 is provably 0.999... (reoccuring)
Here is my favourite proof:
x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1
So x = 0.999... = 1
Fine the error in my math if you want, but you won't since this thing has been known by mathematicians for years
You removed the infinite from the equation when you subtracted it from itself. Essentially, you have cancelled out the effect of infinity. Your problem becomes this:
x=.9^
10x=9.9^
9.9^-.9^=9 (You will notice that you have cancelled out infinity in this step... therefore infinity is no longer a part of the equation.)
9(new x)=9
New x=1
Essentially... this 'proof' is invalid, because you have changed the value of X by canceling out the effect of infinity upon the number. As in, you are no longer proving that the first value of X (.9^)is equal to one... but that the new value (1) is. You changed the value of X when you canceled out part of the equation. Simply, 1-1=0... just as infinity - infinity=0. You negated its effect in your calculation, so that you could solve it without infinity's effect.
You accept that 2*10=20, 20-2=18, no? Then how come when we take 2*9, it is ≠ 18? Essentially, that is what is being done in this 'proof'. Registering different answers for 20-2 and 2*9 is a fallacy under finite circumstance... and is only (and according to some people, not even then) possible when eliminating an infinite or infinitesimal or other undefined number. For example, 10x2.2^-2.2^ would not be equal to 9x2.2^.
x=.9^
9x=8.9^1
8.9^1/9= .9^
Once you nullify the infinite part of x, then you are no longer proving .9^. You are proving a finite by canceling out the infinite. By doing so, you get a different answer for 10x-x, and for simply 9x. If this were a finite number to begin with: you would not get different results from those two normally equivalent expressions. I do not accept this 'proof' of an infinite equalling a finite... for it is only by the canceling of the infinite concept that the inequality can 'solved'.
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