1=.999999...?

[Akka]

I just gave you a real-world-example of this, one that doesn't end with a specific digit.

You can't give a real-world example of infinity, duh.
As it was said several times before, it's the basis of the problem : people don't grasp what "infinity" really represents.

 

[Terxpahseyton]

I
just

did

I'll find more creative ways to write this if need be.

 

[hoplitejoe]

This example was a family which never dies out (which is extremely unlikely, and most likely impossible in practical terms, but not in principle) and generation after generation continues the number of 0.999..., forever.

So which generation of family member reaches 0.999... so you can ask if it is equal to 1?

This wouldn't solve anything, even if it couldn't exist, because there is always someone continually there writing the number.

That's why it can only exist in abstract realm of maths, where you can state it's infiniteness without ever trying to count to infinity, which is of course, impossible. In the real world, you can always go one further, in maths you can just skip that.

 

[Terxpahseyton]

Sorry but you just don't get it. Are you that unable to consider I might be right and the math "wrong" (regarding representing ultimate truth)?
WE KNOW THAT IN ETERNITY THEY WOULD NOT REACH IT. We know that they could do it for LITERAL INFINITY and not reach one. Because the fundamental function of the infinite series and which 0.999.. represents is, just as in each identical part, in the whole not designed to ever reach it. Since it just keeps on repeating a step where math itself says can't make it one no matter how many times.
All you have to say to that is "You don't understand infinity" I suppose I forgot that infinity is magic. So say the word. Or give another explanation.

 

[hoplitejoe]

You are one step ahead of yourself. You are saying that they never reach 1, and are assuming that they can reach 0.999... I am arguing that they could never reach the 0.999... to check it is equal to 1, thus this being your proof to say that 1=.999... false makes no sense, as you don't have the 0.999....

Another thing you should watch out for, is in your experiment you should probably be representing the numbers physically, as written numbers aren't really what you are referring to here.

 

[brennan]

A physically written number is not a physical representation...?

 

[hoplitejoe]

A physically written number is not a physical representation...?

If I write "2+2" the number 4 does not appear.
If I have 2 apples, and I take another 2 apples, I then have 4 apples.

Thought it was worth stating at this point in case there was visions of people writing a string of 9's expecting them to turn into a 1 suddenly.

 

[brennan]

Of course...the impossibility of reality containing 0.999... of something is actually part of our point.

 

[uppi]

Sorry but you just don't get it. Are you that unable to consider I might be right and the math "wrong" (regarding representing ultimate truth)?
WE KNOW THAT IN ETERNITY THEY WOULD NOT REACH IT. We know that they could do it for LITERAL INFINITY and not reach one. Because the fundamental function of the infinite series and which 0.999.. represents is, just as in each identical part, in the whole not designed to ever reach it. Since it just keeps on repeating a step where math itself says can't make it one no matter how many times.
All you have to say to that is "You don't understand infinity" I suppose I forgot that infinity is magic. So say the word. Or give another explanation.

You are essentially saying, that 0.99... does not exist. They would never reach one, but they would also never reach 0.99.... If you are doubting infinity, you should not even ask whether 0.99... = 1, because you do not even accept the premise of 0.99...

 

[hoplitejoe]

Of course...the impossibility of reality containing 0.999... of something is actually part of our point.

Then your objection is not with 1=.999..., is it? If you insisting in kicking out all of maths from the question then the idea of 0.999... is entirely meaningless. Does 1 equal a meaningless thing? The answer is blob.

 

[bhavv]

27. Pages. Dear. Mighty. Lord. FSM. How. Has. This. Happened?

 

[brennan]

Then your objection is not with 1=.999..., is it? If you insisting in kicking out all of maths from the question then the idea of 0.999... is entirely meaningless. Does 1 equal a meaningless thing? The answer is blob.

You agree with me then?

 

[UWHabs]

Interesting to read people's take.

Infinities are incredibly hard to understand. Especially once you get to other points about infinity having multiple sizes, or get to the arguments how there are the "same" number of positive numbers as there are rational numbers, even though one is entirely contained within the other.

But as to the basic point, a big point in favour is that I think most people would agree that the series 1 + 1/2 + 1/4 + 1/8 ... eventually equals 2. At any point in the series the partial sum is less than 2, but if you take it to infinity, then you can get 2 out of it. .999... = 1 in essentially the same way.

 

[hoplitejoe]

You agree with me then?

If you refuse to accept mathematical infinity, then go ahead. Less of a "you are right" more of an "I can't be assed to go off topic this much", but if that means you win, I'm happy for you.

Personally, I'm completely fine with using maths, and infinity within maths. It's something I have used almost constantly while studying physics and the maths surrounding it, and so with 1=.999... and if you don't object to the statement any more I don't really have an issue.

 

[brennan]

Where have I said that I refuse to accept mathematical infinity?

 

[bhavv]

I want this thread to die

 

[hoplitejoe]

Where have I said that I refuse to accept mathematical infinity?

Do you accept 0.999... (an infinitely repeating decimal) to be a meaningful concept,

A)within mathematics
B)within whatever mathematics free world you insist on existing in?

 

[brennan]

I tell you what. Why don't you read my earlier posts and if & when you understand what position i've been taking then you can ask me a question about it. I've had a couple of quite interesting responses. Yours is not one of them.

 

[hoplitejoe]

i'm pretty sure those interesting posts should suffice for you, clearly im not up to the staggering mental ability that you are at

just try and remember what i taught you about writen numbers

 

[Hygro]

could it not simply be an error in the notation we use that allows [our math] to prove that 0.9...=1, even if a difference is functionally meaningless?

This is the third (fourth?) time I'm asking.

I would like to field a second question.

Does "0.999...8" also equal 1? Why or why not?