In our Geometry class, we have been discussing the concept of infinity. What does in mean when we say that numbers are infinite? Can we really understand that? And further, if numbers are infinitely large, does there exist a number that is infinitely small? How do we deal with this "infinite smallness?"
The question that has come up in class is this:
Is .9999... = 1?
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19 comments:
No it doesn't because it is still not one whole
but you can just put the repetent bar over the nine
I may be wrong still because this question is based from a lesson in geometry
I agree with chris because 9 repets so you must put a repaten bar over it - Dil
No. Or at least I think so. There's still that small part that doesn't equal one.
Parker S.
if the question was does 1=1 then it is correct...but if the question was does 0.9999=1 then it isn't true because you need to put repitent bar over the 9 because the 9 repeats itself.
Venesa Gutierrez
periods 2/3
9/5/08
Sup Mr Cox
I was going to put all the online examples on a dvd like you recomended but you didn't give them a burn right. I was just hoping that you could give those videos a burn right so i can put them on a dvd and when it comes time for a semister test i could have all the information on a dvd
Chris Buettner
The concept that numbers are infinite means that these number will go on forever, nevering reaching a destination, it is something that just is inconperhensible. There must be a number that is infinitely small, because there is a number that is infinitely large. Since I have established this idea on an infinite large number, we cannot question that 1=1, based on this line of thinking. We must think of the right questions that will enable us to just grasp the concept of infinity in order to answer this question correctly.
-Austin Kittrell
Please disregard my first responce.
The concept that numbers are infinite means that these number will go on forever, nevering reaching a destination, it is something that just is inconperhensible. There must be a number that is infinitely small, because there is a number that is infinitely large. This number will continue to get infinitely smaller, but yet we know that somehting can always become even smaller, not enabling us to truely even comprehend it. I feel obligated to say the answer would have to be, yes 1=1.
-Austin Kittrell
I agree with chris, dil, and venessa because only 1=1 not 0.99999999999999999999999999999999999999999999999999... so i think the answer is no because of the fact that 1=1.
-from breanna c
period 2-3
.9999999999999... doesn't equal to one, it is close but it still not a whole one.
-Fareen
Remember that .999... goes on forever. So if .999... isn't equal to 1, then how far is it from 1?
Mr. Cox
.01 is the distance for your question Mr. Cox
Dil
Can that be correct if the number is .99999999999...?
Mr. Cox
Mr. Cox/Dil
then wouldn't it be .11111...???
-Fareen
then I think that it should be 0.01 with a repaten bar over the 0 after the decimal point
0.000000000000000000000001 is the answer to your other question Mr.Cox.
Venesa Gutierrez
periods 2/3
9/10/08
hi i think that .9999... is not equal to one as a stated in class, because even though it gets so close to one it basically equals one, i think there has to be a number in between them. And some of the students were saying "well, if 1/3=.3333.... and 2/3=.6666.....then wouldn't 3/3=.9999...." but it doesn't equal .999...., it equals 1. So i don't think .999... equals one.
eva
oh and i think the smallest number is the greatest number only negative Mr. Cox So infinity both ways after Zero.
eva
I say it does cause I don't want to have another "heated debate" durring 6-7 period and because 3/3 equals one whole, .99999... is so infinantly close to 1 that it is indistinguishable from 1
-Alex G
I think that the answer is no because .99999999999(ext.) doesn't equal 1, which is a whole number. Another idea I have is since the number goes on with 9's, it could be yes because then you would end up rounding the number to the nearest whole, which is one. However, since you are asking
if .9999999 (ext.) is (not a whole number)equal to one, my answer would have to be no.
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