The .9999... Debate: Is it Really Equal to One?

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In summary, there is a common argument about whether or not 0.999... is equal to 1. However, this topic has been widely discussed and there are at least 20 threads on it. Those who argue against it typically have a limited understanding of mathematics. According to the axioms of real numbers, 0.999... is indeed equal to 1 and any attempts to redefine the real numbers are not accepted. This topic has been closed by WarrenHurkyl in another thread.
  • #1
sublime
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0.99999... = 1

From what I have read and understood .999... = 1. Wherever I read it, I notice a huge argument sparked. What does everyone think.
 
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  • #2
There are at least 20 threads on this topic, so I suggest you browse first.
 
  • #3
Come on... not again. This is neither an interesting nor challenging topic for anyone with more than a school child's grasp of mathematics. The only people who argue it are, well, those with no more than a school child's grasp of mathematics. There is no argument -- 0.999... = 1 by the axioms of the real numbers. Unless you're trying to redefine the real numbers, there is no possible way that 0.999... does not equal 1. If you're interested in redefining the real numbers, well, we're not interested in listening. End of story.

- Warren
 
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  • #4
Hurkyl just closed this exact thread in "Number Theory".
 
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What is the .9999... Debate?

The .9999... Debate is a mathematical discussion about whether the infinite decimal representation of 0.9999... is truly equal to one.

Why is this debate important?

This debate is important because it challenges our understanding of numbers and the concept of infinity. It also has practical applications in fields such as mathematics, physics, and computer science.

What is the evidence for and against 0.9999... being equal to one?

For: One of the main arguments for 0.9999... being equal to one is that it is a mathematical fact. The infinite decimal representation of 0.9999... is a geometric series that converges to one. Additionally, it can be proven using algebraic manipulation.
Against: Some argue that 0.9999... is not truly equal to one because it is an approximation and never reaches the exact value of one. Others argue that the concept of infinity is not well-defined and therefore cannot be used to prove equality.

What are some real-life examples that support 0.9999... being equal to one?

One example is the decimal representation of the fraction 1/3, which is 0.3333... By multiplying this fraction by 3, we get 0.9999..., which is equal to one. Additionally, some computer systems use 0.9999... to represent the maximum real number value.

What is the conclusion of this debate?

While there is still debate and differing opinions, the majority of mathematicians and scientists agree that 0.9999... is equal to one. However, it is important to note that this concept may continue to be debated and explored in the future.

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