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killerinstinct
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Very common debate: is 0.999999 repeating 1?
Opinions?
Opinions?
killerinstinct said:Very common debate: is 0.999999 repeating 1?
Opinions?
JonF I have never been on any mesage board where there have not been arguments about this and that includes non-maths/sci boards.JonF said:This has to be the most asked question on this forum.
On any bulletin board, no matter the subject area of that board, sooner rather than later someone will argue that 0.99.. is not equal to one.
I must say I dislike these kind of comments. I am a 16 yr old student who has not taken a lot of math, certainly not on the subject of infinity. I fail to see why you would judge me as "a last little bit poster" or whatnot, for simply voicing a (to me) logical view. Though these thing may be obvious to you, that is not so for everyone. I find that your post without the two first lines would have been completely satisfactory.Integral said:I knew it.^~ A last little bit poster would have to show up. Do we try to explain it to him?
Grizzlycomet said:I must say I dislike these kind of comments. I am a 16 yr old student who has not taken a lot of math, certainly not on the subject of infinity. I fail to see why you would judge me as "a last little bit poster" or whatnot, for simply voicing a (to me) logical view. Though these thing may be obvious to you, that is not so for everyone. I find that your post without the two first lines would have been completely satisfactory.
Thank you, apology accepted :) I understand that you may have seen this question many times, thus growing very tired of it. Your explanation was in itself good :)Integral said:My apologies, having been involved in this same discussion on several different forums over the last 2 or 3 years I do not recall anyone ever saying "oh I see" so perhaps am a bit cyncial about the whole issue.
Integral said:I knew it.^~ A last little bit poster would have to show up. Do we try to explain it to him?
That "last little bit" is [tex] \frac 1
\infty [/tex]. By the definition of infinity, that last little bit is zero. So essentially this is true by definition, but beyond that it is completely consistent and provable in many different manners. There is no law that says each point on the real number line must have a unique representation. In fact just the opposite is true, every point on the real number line has many (perhaps an infinite) number of different ways to represent it.[/QUOTE]
Whoa there! In the emphasis added section above, I don't understand what you're getting at. Are you referring to different bases? If we stick with only a single base, don't all irrational numbers have one and only one representation? Rational numbers can have two representations, a "finite" form "a.bcdef000..." where the infinite series of zeroes at the end are ignored, and "abcde(f-1)999..." Much like the inverse of the question of this thread. I'm hazy about this, but I vaguely remember that the representation of some numbers are unigue, and the representation of others are not unigue but have exactly two forms, as being critical to some fundamental proof Cantor used in developing his theories.
The only thing I'm sure about is that I didn't understand it at the time, and had to go on to other things. Regretably, I never got back to it. Does anyone know more clearly what this was? As it was fundamental, might that serve as a good argument when this topic rears it's cursed ugly head again, as it surely will?
If we stick with only a single base,
TENYEARS said:It is a real number, but it will never be complete. It is not 1. One is be, but be is not .99... You will always be chasing your tail.