Instigator / Pro
56
1554
rating
15
debates
73.33%
won
Topic

0.999... = 1

Status
Finished

All stages have been completed. The voting points distribution and the result are presented below.

Arguments points
24
0
Sources points
16
12
Spelling and grammar points
8
6
Conduct points
8
0

With 8 votes and 38 points ahead, the winner is ...

Nemiroff
Parameters
More details
Publication date
Last update date
Category
Education
Time for argument
Three days
Voting system
Open voting
Voting period
One month
Point system
Four points
Rating mode
Rated
Characters per argument
10,000
Contender / Con
18
1294
rating
75
debates
18.0%
won
Description
~ 0 / 5,000

No information

Round 1
Pro
How to convert a repeating decimal into a fraction: https://studymaths.co.uk/topics/convertingRecurringDecimalsToFractions.php

X = 0.333... 
10x = 3.333....
10x - x = 3.333... - 0.333...
9x = 3
X = 3/9 = 1/3
0.333...  = 1/3


X = 0.111...
10x = 1.111...
10x - x = 1.111... - 0.111...
9x = 1
X = 1/9
0.111... = 1/9

X = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
X = 9/9 = 1

Con
Nonsense 1 is greater than anything less than one even by a bit
Round 2
Pro
1 is greater then anything less then 1, even by a bit. But 0.999... is clearly = to 1. And anything equal is not less then 1, even by a bit.

0.333 is not 1/3rd. 0.333333333 is not 1/3rd.
0.3 and any finite number of zeros is still less then 1/3rd. Even if there are billions of trailing 3's, still less then 1/3rd (even if by only a bit).
But 0.3 with *infinite* 3s is 1/3rd.
Just like 0.9 with *infinite* 9s is 1.

Your error lies in the fact that infinity is not a number. Infinity is not simply alot of 9s. Its never ending. To infinity. If 0.999... =/= 1, then 0.333... =/= 1/3, which it most certainly does.

And finally, appeals to logic are always weaker then objective fact, like a mathematical proof. Heres another proof:

0.333... = 1/3
0.333... (x3) = 1/3 (x3)
0.999... = 3/3 = 1
Con
you are splitting hairs , literally!
Round 3
Pro
Disagree. This is not a question of semantics or anything like that. This is fact, as certain as 1 = 1.

I thought that 10x in my original formula was conveniently easy. If it is an iron fact rule, any multiplication of both sides of the equation should work.

First i tried 5, assuming wrongly that 5x would be half of 9.9999999.... as 4.5454545.... forgetting to carry remainders. If you punch in 0.99999 ×5 into a calculator you will get 4.99995. Add more 9s, the answer adds more 9s. No other changes. So assuming infinite 9s, 5x would be 4.99999.... and the final 5 would never come. Thus:

X = 0.999...
5x = 4.999...
5x - x = 4.999... - 0.999...
4x = 4
x= 4/4=1

Again with 3.

3x=2.999...
3x-x=2.999... - 0.999
2x=2
X=1

Again with 23
23x= 22.999...
22x=22
Con
Forfeited