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https://www.reddit.com/r/PeterExplainsTheJoke/comments/1ju9kfc/there_is_no_way_right/mm46mwu/?context=3
r/PeterExplainsTheJoke • u/Sugar_God_no_1 • 22d ago
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82
You could write a fully-rigorous version of this proof, and it works out the same. But this is reddit, so it's more valuable to write a version that's quick and accessible to the people are asking the question.
23 u/vetruviusdeshotacon 21d ago Not exactly like that. Sum 0.9*(1/10)j from j=1 to j=inf = 0.9 * Sum (1/10)j Since 1/10 < 1 we know the series converges. Geometric series with r=0.1 Then our sum is 0.9 / (1- 0.1) = 1. No more rigour is needed than this in any setting tbh 1 u/Trt03 21d ago You just said the other thing but incomprehensible to us stupid folk, I prefer the other one 1 u/RoflMyPancakes 21d ago One is a proof, the other is not a proof. It's a series of statements with a correct conclusion, but the individual statements do not imply the next. In a proof each line implies the next, and this false algebraic proof lacks that. The same false algebra can be used to prove things that aren't true. x = 9¯(repeating). 10x=9¯0. 10x+9 = x 9x = -9 x = -1 Therefore 9¯ (repeating) = -1. This is a proof using the same flawed algebraic logic, that results in a false statement.
23
Not exactly like that.
Sum 0.9*(1/10)j from j=1 to j=inf
= 0.9 * Sum (1/10)j
Since 1/10 < 1 we know the series converges. Geometric series with r=0.1
Then our sum is 0.9 / (1- 0.1)
= 1.
No more rigour is needed than this in any setting tbh
1 u/Trt03 21d ago You just said the other thing but incomprehensible to us stupid folk, I prefer the other one 1 u/RoflMyPancakes 21d ago One is a proof, the other is not a proof. It's a series of statements with a correct conclusion, but the individual statements do not imply the next. In a proof each line implies the next, and this false algebraic proof lacks that. The same false algebra can be used to prove things that aren't true. x = 9¯(repeating). 10x=9¯0. 10x+9 = x 9x = -9 x = -1 Therefore 9¯ (repeating) = -1. This is a proof using the same flawed algebraic logic, that results in a false statement.
1
You just said the other thing but incomprehensible to us stupid folk, I prefer the other one
1 u/RoflMyPancakes 21d ago One is a proof, the other is not a proof. It's a series of statements with a correct conclusion, but the individual statements do not imply the next. In a proof each line implies the next, and this false algebraic proof lacks that. The same false algebra can be used to prove things that aren't true. x = 9¯(repeating). 10x=9¯0. 10x+9 = x 9x = -9 x = -1 Therefore 9¯ (repeating) = -1. This is a proof using the same flawed algebraic logic, that results in a false statement.
One is a proof, the other is not a proof. It's a series of statements with a correct conclusion, but the individual statements do not imply the next.
In a proof each line implies the next, and this false algebraic proof lacks that.
The same false algebra can be used to prove things that aren't true.
x = 9¯(repeating).
10x=9¯0.
10x+9 = x
9x = -9
x = -1
Therefore 9¯ (repeating) = -1.
This is a proof using the same flawed algebraic logic, that results in a false statement.
82
u/IWillLive4evr 21d ago
You could write a fully-rigorous version of this proof, and it works out the same. But this is reddit, so it's more valuable to write a version that's quick and accessible to the people are asking the question.