Do you ever stop to think about the fact that ".9 repeating" is just another way to say 1? I have to admit that I do, so I found this wonderful. If you're a nerd like me, be sure to browse the hundreds of comments on that guy's site.
As fun as .9-repeating is, it's not as wonderful as the fact that neighboring numbers in the fibonacci sequence tend toward the golden ratio, phi.
Sally thinks of me as a math nerd, but I'm really not. I don't know very much about math, so when I do think about it, simple things like the two facts above fascinate me. It doesn't take long before I'm out of my depth.
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8 comments:
Sally, it's okay
Very interesting (another math nerd here). At first I was taken by the explanations on the blog, but I think his number line theory is his undoing. .9 repeating must be a separate number from 1, admittedly in order to perform mathematical functions with such a number it must be rounded and rounding .9 repeating anywhere before infinity will produce 1. However, .9 repeating must have its own place on a number line and that place is the position infinitely close to 1 without quite reaching 1. His algebraic "proofs" are interesting, but the fraction example in particular only works because the numeric representations of the fractions are imperfect. Dave here btw.
If you accept that 1/3 is equal to .333..., then I don't see why you have a problem with 3/3 being equal to .999....
test
i would like to consider this in terms of the beloved and long-running television gameshow, "The Price is Right." 0.999... is the closest without going over, or in this case, without equalling one. admittedly, although not always apparently, however, i am an English--not a math--nerd, so i have no way of supporting my assertion.
one question: if, 0.999... IS, in fact, equal to 1, then is 1.000...1 also equal to 1? just asking. and, please, i really do not want to know.
Trace - I know it's completely non-intuitive, but .999... is actual equal to one. It's not the closest you can get without equaling one, it's actually one.
And yes, 1.0 is also equal to one. It's another way to write the same thing, just like 3/3.
I think there are two general ways of looking at it. One is that if 1/3 = .33..., then 3/3 = .99... . The other is based on number density: the idea that every two distinct numbers has a number in between them. If 1 and .99... are distinct numbers, then what number is in between them?
did i mention that i don't care? just checking. it is truly shocking what gets people goin on these blogs.
and by the way the number between .99 and 1 is 0.000000000000000000000000000000000
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0000000000000000000plusawholebunch
more,aninfintenumberactually,zeroesandthena1.
ok, i get your point. it was just a theory, jeez...love y'all
all is forgiven....
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