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Originally posted by Zurahn
FALSE. Division by infinity DOES NOT EQUAL ZERO. It's an infintesimally small number, NOT ZERO.
THEREFORE 0.9r CANNOT EQUAL 1
Kepp in mind: In all practical use, division by infinity is simply assumed to be zero, but we're not talking about practical use, we're talking about exact precision of a number.
Originally posted by gfad
Originally posted by Zurahn
FALSE. Division by infinity DOES NOT EQUAL ZERO. It's an infintesimally small number, NOT ZERO.
THEREFORE 0.9r CANNOT EQUAL 1
Kepp in mind: In all practical use, division by infinity is simply assumed to be zero, but we're not talking about practical use, we're talking about exact precision of a number.
This statement is where your problem comes in. The division by infinity DOES equal zero. If you can find a proof for that statement then you have prooved me wrong but I dont think you can.
An infinitely small number is zero. Dividing by a very large number will get you a very small number but infinity isn't a number at all, its a concept. If you describe a infinitely small number as 0. followed by an infinite number of zeros then 1, then you will never get to that 1. The zeros continue forever and the infinitely small number is just 0.0000000000...
Originally posted by gfad
Originally posted by Zurahn
FALSE. Division by infinity DOES NOT EQUAL ZERO. It's an infintesimally small number, NOT ZERO.
THEREFORE 0.9r CANNOT EQUAL 1
Kepp in mind: In all practical use, division by infinity is simply assumed to be zero, but we're not talking about practical use, we're talking about exact precision of a number.
This statement is where your problem comes in. The division by infinity DOES equal zero. If you can find a proof for that statement then you have prooved me wrong but I dont think you can.
An infinitely small number is zero. ...
Originally posted by Zurahn
That's not the one to which I'm referring. The problem with the "old proof" you posted is that 10 * .999 = 9.99 not 9.999. This is for .9 repeated, which is more complicated.
Originally posted by T_Jesus
Algebraic proofs are not solid mathematical proofs due to the nature of infinities used in a repeating decimal. It would be more appropriate to use limits, sequences/series, and best of all uniform convergence.
However, I do not fully grasp the concept of 0.9r equally to one - I understand it property wise but the techniques used to prove it on Wikipedia aren't exactly the strongest proofs I can think about. I'm also thinking about mapping - I am no expert in the field as I've only taken one Analysis course so I'm going to ask an Analysis professor about this.
By the way, I think it's unfair to flame someone for attempting to understand a concept. You may have a million ways to prove something, but nothing is greater than only one way to disprove something.
Originally posted by Zurahn
9.9... - .9... only equals 9 if infinity is a constant, which it is not. The number of decimal places isn't necessarily equal, therefore .9... - .9... isn't necessarily zero, which is the problem with writing .9... as a decimal in the first place.
Originally posted by Zurahn
For example, here's what you are doing under a fractional form, using my 1 - (1/i) form
x = 1 - (1 / i)
10x = 10(1 - 1/i)
10x - x = 10 - 10/i - (1 - 1/i)
9x = 10 - 1/i - 1 + 1/i
9x = 10 - 1 + 1/i - 1/i