Largest Number in (0,1)? PF's Take

  • Thread starter JCienfuegos
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In summary, since 1 = 0.999..., the open interval (0,1) does not have a largest or smallest element. This is because it is not possible to have a largest or smallest element in an interval that includes all numbers between 0 and 1, including 0.999... itself. The concept of a smallest or largest number in this interval is contradictory and does not make sense.
  • #1
JCienfuegos
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Since we all agree that 1 = 0.999..., what does PF think the largest number in the open interval (0,1) is?
 
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  • #2
What do you think the smallest number in the interval is?
 
  • #3
JCienfuegos said:
Since we all agree that 1 = 0.999..., what does PF think the largest number in the open interval (0,1) is?

Just because you can ask a question, doesn't mean there is an answer. (0,1) doesn't have a largest element. It's as simple as that.
 
  • #4
I always imagined that the smallest number less than one was the infinitesimal 0.9..., but that cannot be, because that equals one. The only other answer I could come come up with was that only terminating decimals of the form 0.999...9 would be in the interval, but that's no good either.

I guess the smallest number would be of the form 0.000...01 and it too would be non-terminating.
 
  • #5
JCienfuegos said:
I guess the smallest number would be of the form 0.000...01 and it too would be non-terminating.
But that number appears to terminate. Is there anything after the 1?

You are overthinking this. We agree that (0,1) does not contain 0. So suppose it has a minimum, call it M. This is a positive number. Then M/2 is a smaller positive number. This is a contradiction, so there is no minimum after all.
 
  • #6
The open interval (0, 1) has NO largest or smallest member. You cannot talk about "the form 0.000...01 and it too would be non-terminating". If is non-terminating, it does not have a last digit so you cannot assert that it is 1.
 

FAQ: Largest Number in (0,1)? PF's Take

What is the largest number in the range (0,1)?

The largest number in the range (0,1) is 1. This is because the range does not include 0 or 1, making 1 the highest possible number within the range.

Why is the largest number in the range (0,1) not 0.1?

The largest number in the range (0,1) is not 0.1 because the range does not include the endpoints. This means that 0.1 is not included in the range and therefore cannot be the largest number within it.

Can there be a number larger than 1 in the range (0,1)?

No, there cannot be a number larger than 1 in the range (0,1). This is because the range is defined as not including 1. Therefore, 1 is the highest possible number within the range.

Why is it important to understand the largest number in the range (0,1)?

Understanding the largest number in the range (0,1) is important because it allows for a better understanding of the properties and limitations of the range. It also helps in making accurate calculations and comparisons within the range.

How is the largest number in the range (0,1) relevant in scientific research?

The largest number in the range (0,1) is relevant in scientific research when dealing with values that fall within this range. It helps in setting boundaries and making accurate measurements and predictions. For example, in probability and statistics, the range (0,1) is commonly used to represent probabilities and the largest number within this range represents the highest possible probability.

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