0.999999… = 1, amirite?

Skepticism in education Students are often "mentally committed to the notion that a number can be represented in one and only one way by a decimal." Seeing two manifestly different decimals representing the same number appears to be a paradox, which is amplified by the appearance of the seemingly well-understood number 1.[35] Some students interpret "0.999…" (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 "at infinity". Intuition and ambiguous teaching lead students to think of the limit of a sequence as a kind of infinite process rather than a fixed value, since a sequence need not reach its limit. Where students accept the difference between a sequence of numbers and its limit, they might read "0.999…" as meaning the sequence rather than its limit.

by Anonymous 13 years ago

0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 = almost 1

by Anonymous 13 years ago

This probably comes from that one group/page on Facebook that says that since 1/3 and 2/3 = 3/3 (1), .33333333 + .6666666 = .999999 (1). However... .3333333 eventually ends with a 4, and .6666666 eventually ends with a 7, so it comes out to round out to 1, or 1.000...1.

by Anonymous 13 years ago

.33333334 + .66666667 = 1.00000001 OMG .99999999 > 1 !!!!! It all makes sense now.

by Anonymous 13 years ago

1/3 doesn't eventually end in 4, nor does .666666...7+.333333...4=1. 2/3 eventually ends in 7 because you round up, but you can't round up .3 because it can never be more than 5. However, .666666...7+.333333... DOES equal 1.

by Anonymous 13 years ago

There is a mathematical proof that demonstrates this post as true.

by Anonymous 13 years ago

Let's sloppily program the computer of infinite digits. X = 1 1 + X = Y If Y = 2 then Youwin = true else Youwin = false Y = 2 Youwin = true X = 0.9999999 1 + 0.9999999 = Y If Y = 2 then Youwin = true else Youwin = false Y = 1.9999999 Youwin = false

by Anonymous 13 years ago

here is how its REALLY done: x = .99999... 10x = 9.99999... 10x - x = 9x = 9.99999... - .99999... = 9 9x = 9 x = 9/9 = 1 QED

by Anonymous 13 years ago

x = 0.9999999999... 10x = 9.9999999999... 10x (9.9999...) - x (0.9999...) = 9x (9) if 9x = 9 then x = 1 therefore 0.9999... = 1 fml beat me to it ^^ @245762 (Anonymous):

by Anonymous 13 years ago

why do u get to arbitrarily subtract x in that equation at 10x (0=9.999...) -x (0.9999...) etc

by Anonymous 13 years ago

He subtracted it form both sides...

by Anonymous 13 years ago

oh he just didnt show it. still... i stand on my laurels.... 1 = 1 .9999...=.9999...

by Anonymous 13 years ago

You sound exactly like my math teacher, with the QED included. Trust me, that's a good thing :)

by Anonymous 13 years ago

Or you could think of it as 1-0.99999... = 0.00000000...1 The zeros would go on infinately, so you would never reach the one. Therefore 1-0.999999... = 0, and 1=0.9999999 :)

by Anonymous 13 years ago

it is not EQUAL to one it is ROUNDED to one to make the math easier(:

by Anonymous 13 years ago

This is the nerdiest string of comments I've ever seen.

by Anonymous 13 years ago

Mathematically I suppose it is, based on some of the comments, but in terms of value, it's not.

by Anonymous 13 years ago

equals means the same, and it's not the same.

by Anonymous 13 years ago

It is the same. Look at it this way. .1111111111111111... is 1/9 .2222222222222222... is 2/9 .3333333333333333... is 3/9 (1/3) and so on. therefore .9999999999999999... is 9/9 = 1

by Anonymous 13 years ago

Did you not read the first post about skepticism in education.

by Anonymous 13 years ago