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A good engineer will tell them that they are wasting their time.This is one of those issues that display the clear distinction between a good philosopher and a expert mathematician.
A mathematician and an engineer are sitting at a table drinking when a very beautiful woman walks in and sits down at the bar.
The mathematician sighs. "I'd like to talk to her, but first I have to cover half the distance between where we are and where she is, then half of the distance that remains, then half of that distance, and so on. The series is infinite. There will always be some finite distance between us."
The engineer gets up and starts walking. "Ah, well, I figure I can get close enough for all practical purposes."
James S Saint wrote:Currently Wiki, and a great many mathematicians will tell you that 1 = 0.999.... Many "proofs" are displayed to show how wrong those are who disagree. The "good philosopher" can display how every one of those proofs are fallacious.
What is your belief?
Wiki wrote:From Wikipedia, the free encyclopedia
In mathematics, the repeating decimal 0.999… (sometimes written with more or fewer 9s before the final ellipsis, for example as 0.9…, or in a variety of other variants, denotes a real number that can be shown to be the number one.
The repeating decimal continues with an infinite number of nines.
In other words, the symbols "0.999…" and "1" represent the same number. Proofs of this equality have been formulated with varying degrees of mathematical rigor, taking into account preferred development of the real numbers, background assumptions, historical context, and target audience.
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Although these proofs demonstrate that 0.999… = 1, the extent to which they explain the equation depends on the audience.
James S Saint wrote:
But their claim is that 0.999 ... is not an irrational number
surreptitious57 wrote:James S Saint wrote:
But their claim is that 0.999 ... is not an irrational number
I thought it was because it has infinite decimal places. However that alone does not make it irrational
according to Wikipedia because it has to be random or non repeatable too such as with pi for example
In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.[1] Since q may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q (or blackboard bold Q {\displaystyle \mathbb {Q} } \mathbb {Q} , Unicode ℚ);[2] it was thus denoted in 1895 by Peano after quoziente, Italian for "quotient".
The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for any other integer base (e.g. binary, hexadecimal).
It can be expressed as the fraction 9/9So 0.999... is technically a "rational number".
phyllo wrote:It can be expressed as the fraction 9/9So 0.999... is technically a "rational number".
surreptitious57 wrote:I have to correct myself when I said I did not think 0.999 ... is equal to I because they are the same number just expressed differently
The Wiki proof is correct and is accepted by mathematicians. It does appear counter intuitive but that does not actually make it false
If you say so then it must be no.Emmmm....
.. no.
phyllo wrote:Why sum an infinite number of numbers when you only need to sum 9?
1/9+1/9+1/9+1/9+1/9+1/9+1/9+1/9+1/9=1
Represented in decimal form :
.111_ + .111_ ... = .999_ and also = 1
That's it in a nutshell. No infinite series required. KISS
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