Thread: Is 0.999... equal to one?

Ahhh, I think I get it.
So the trailing 9 in 0.999... is also irrelevant
and what about the 9 before that (hypothetical) 9
is infinity -1 the same as infinity +1
no, lost it again...

Originally Posted by TaoZero5

is infinity -1 the same as infinity +1

Of course! That's my answer anyway.

no, lost it again...

Because of that? What is your answer?

Yep, that was my answer too.
...and so, the infinite number of decimal places fall, one by one, into the black hole of Infinity,(,,,)
but - where is the event horizon?
If I keep reducing the number of decimal places - it remains an infinite number ???
ad infinitum (or, in this case, subtract infinitum)

There is no black hole.

Interesting attempt at an analogy though. The reason analogies don't work in math is that all of math is an analogy. You have to work within that analogy, it's seldom easy to mix them.

In this instance, the digits aren't falling into an event horizon one by one--as soon as we write ".111..." all the digits are in their place, we're just trying to understand what it could possibly signify.

Originally Posted by grapes

In this instance, the digits aren't falling into an event horizon one by one--as soon as we write ".111..." all the digits are in their place, we're just trying to understand what it could possibly signify.

Although I do agree with this, it seems like how we arrive at 'what is' in maths, is by process, and maths is used to describe and define dynamic processes.
It may be that all of space/time exists, or that space exists now - either way, can we define any instant fully, without looking to include information from both the past and the future.

Originally Posted by grapes

Then, if we push this out far enough, so that in our scheme of things, there are an infinite number of ones (that's what the trailing ellipsis ... represents), the "position" of the two would have to be infinite.

What possible interpretation of the value of 2/10^N can we make, if N is infinity? Clearly, if N is infinity, 10^N is also. So, what can we say about 2 divided by infinity?

Ok, I understand this
But I was under the impression that the trailing ellipsis ... in these scenario's state nothing more than that the trailing decimal continues on for ever. Your explanation although clear and precise changes the meaning of the ellipsis so to have its own value of infinity?

Yes, in some schemes, .888...1 and .888...2 (with the ellipsis representing an infinite number of 8s) would be actual different numbers. However, in the usual scheme, both of those would be equal to, and represented by, .888..., by the reasoning in my other post.

Originally Posted by grapes

Yes, in some schemes, .888...1 and .888...2 (with the ellipsis representing an infinite number of 8s) would be actual different numbers. However, in the usual scheme, both of those would be equal to, and represented by, .888..., by the reasoning in my other post.

Now surly you knew that I would see this and not 'like' it. At some point that 888...1 can not be said to be of actually equal value of the 888...2.

To make that premise as you have.. IS WRONG. regardless of you mathematics based logic. Wrong is wrong is wrong... 1 does not equal 2.

That 888... is a different value. Is fact, regardless of how small that difference might be. I see three different numbers. ... and ...1, ...2 Don't you ?

Originally Posted by astromark

Now surly you knew that I would see this and not 'like' it. At some point that 888...1 can not be said to be of actually equal value of the 888...2.

Did you think I'd not want you to see it?

To make that premise as you have.. IS WRONG. regardless of you mathematics based logic. Wrong is wrong is wrong... 1 does not equal 2.

1 does not equal 2. I agree with that, but 1/143 does equal 2/286. The denominator makes a difference. We are talking about decimal fractions, not just 1 and 2.

That 888... is a different value. Is fact, regardless of how small that difference might be. I see three different numbers. ... and ...1, ...2 Don't you ?

Regardless of how small that difference is? Surely you don't mean that--what if the difference is zero?

Which it is.

I would have thought you might jump on that number.. and the completely wrong expression of it..

888... is a infinitival stream of 8's. adding a 1 or 2 to the end of that ... does not make any sense.

and that would be because the ... gives indication of a infinite term.