Does 0.999... Equal 1?

[Menago KF]

steven787 said:

Menago KF said:

steven787 said:

Menago KF said:
Generally it does.

Put it this way: 0.9999.....does not equal 1, BUT

0.(9) is equal one. So one someone aska you what 1/3 is in numbers you give the answer 0.(3) . Multiply 0.(3) by three and that is equal to 1/3 times 3. And that equals one.

If someone doesn't get what i'm saying, when you write some number like 0.9999999........... ==> that does not mean that the number is infinate. It ends at some distant point that you can't accurately pinpoint, but it still ends.

In this case the () with a number inside means that the number goes on for infinity.

And because 0.(9) goes on for infinity, it is so close to the actual 1 that it is percieved to be that number.

 

Thank you.  But I don't like the wording of the last sentence. Perception may matter when measuring a circle for a drawing or building.  But when working sets of data, a lot of precision is lost.

1/3+1/3+1/3 = 1 and .(3) + .(3) + .(3) = .(9) no big deal.

but when you have 1/3 + 2/7 + 6/11 + 4/13 + 9/17 + 3/23 = .... that would lose a lot of accuracy if you convert each component to a decimal before adding them up.

 

Of course, but i was speaking of this one particular subject. The one you brought up is a completely different matter and should be solved accordingly.

As to the wording: i had maths in Polish, not English, excuse my lack of accurate wording on the subject. I cannot agree with the first part of your post though.

If anything, with this set of data, this kind of simplifying is a must, or else you would have gone haywire trying to  calculate precisely. When your making measurements of some kind of mathemetical object, there is no way to do it "on a hunch of perception" , you have to do it by the established equations.

 

I agree, but it depends on the idea of simplification.  Using numerical symbols (to avoid fractions), rounding, etc is easier for some, and keeping original forms and having exact answers is easier to others.

The problem is, in the OP, there is a flaw.  .(3) ~= 1/3

That's my story and I'm sticking to it.

 

I take it that you mean my OP about 0.(3)=1/3.

Of course you are right that 0.(3) is more like ~=1/3 but the same thing goes with 0.(9) which is actually ~1.

The thing is, that this has been decided by people smarter than us or two ioi's put together. It's mathemetical law, and you have to abide by it. It's not debatable i'm afraid. Trust me, i don't like the idea either, but whenever i would raise such a topic in math class in high school, i would get this answer: It's not debatable.

Edit: point of my rant about math law==> if 0.(9)=1 then 0.(3) will be equal to 1/3.