I would love to hear your thoughts on this intriguing topic!

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In summary, the concept of 0.999... being equal to 1 has been a topic of debate and discussion, but based on mathematical principles and arguments, it can be considered a fact. This has been discussed extensively in various forums and threads.
  • #1
Nick89
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0.999... = 1 ??

Hey,

I was just reading about this and thought it was interesting.

Apparently, from what I have read, 0.999... = 1
(where the 999... represent an infinite series of 9's)

There were a few good arguments for this 'fact' and also a few arguments against it...

What I want to know is, is this actually true, a fact, or merely a 'theory' ?

Is 0.999... = 1 just as valid as 1+1 = 2 ?
 
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  • #2
Yes it is. Please search the forums for other threads on this. You will see that it has been discussed here extensively.
 
  • #3

1. What is the proof that 0.999... = 1?

The proof for this statement is based on the fact that the decimal representation of a number is not unique. In this case, 0.999... and 1 both represent the same value, and thus can be considered equal.

2. How can a number with infinitely repeating decimals equal a whole number?

This can be counterintuitive, but it is important to remember that our traditional decimal system is just one way to represent numbers. In other systems, such as the binary system, 0.999... does not exist and 1 is the only way to represent this value. The concept of infinity makes it possible for these two seemingly different representations to be equal.

3. Can this be proven mathematically?

Yes, there are several mathematical proofs that show 0.999... is equal to 1. One of the most common proofs is based on the concept of limits in calculus, which shows that as the number of 9s in 0.999... increases infinitely, it approaches 1.

4. Is this true for all numbers with infinitely repeating decimals?

No, this statement only applies to numbers with infinitely repeating decimals that are equivalent to a whole number. For example, 0.333... is not equal to 1, but 0.333... can be written as the fraction 1/3.

5. Why is this concept important in mathematics?

The concept of 0.999... = 1 is important because it challenges our understanding of numbers and how we represent them. It also demonstrates the power and complexity of mathematical concepts such as infinity and limits. Additionally, this concept is used in many mathematical proofs and applications, making it a fundamental concept in mathematics.

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