Is 1 = 0.999... ? Really?

I know I sound like an incomrehensible crazy person…

I’m working again on the 0.999… /= 1 argument, and if as Magnus states, silhouette is the “ecmandu whisperer”…

It’s a lot to ask silhouette, but can you help me disprove your proof that 0.999… does equal 1!!!

My argument is this:

The number 1 never occurs with the infinitesimal argument … thus, the 0.999… never falls like dominoes from right to left to create the whole number from the infinite sequence. Are we good so far??

So next, this means the only other option is to carry from left to right.

This means that you have to add 0.999… to 0.111…

The first time you do this you get 1.0999… and 1.0111…

The second time you do this, you get 2.10999…

See where I’m going with this sil???

Like I stated before, if you have no infinitesimal and the only other option is to carry from left to right, you have no equality for 1=0.999…

So, Silhouette! I’m asking you to “man up” here, and consider my argument is true.

So we have two infinite parallel lines that are of the same length. We pick one of them and remove every odd inch from it. Then we fill in the gaps that we created using remaining inches. By doing this, the gaps disappear leaving the two lines looking perfectly identical.

The problem is that there isn’t enough inches remaining to fill in the gaps without creating new gaps elsewhere. This illusion is created by moving the gaps out of our sight.

If you don’t see it, it’s not there.

And if you keep pushing things out of your sight, you can keep reassuring yourself they don’t exist.
Especially if this process is an infinite one (:

Here’s the line we started with:
( \bullet \bullet \bullet \bullet \bullet \bullet \cdots )

Now here’s the line with odd inches removed from it:
( \circ \bullet \circ \bullet \circ \bullet \cdots )

There’s an infinite number of inches out of our sight. We don’t see them, we merely see the ellipsis “…” which tells us there is more to this line than what we see. What we want to do now is take three inches from the remaining inches that we don’t see, so that we can fill in the gaps. We can do that, because there’s still an infinite number of inches remaining, so we do that and we get:

( \bullet \bullet \bullet \bullet \bullet \bullet \cdots )

Voila! The line looks like the original one! They now appear to be identical! But what happened to those gaps? Where did they go? Well, they went out of our sight. They didn’t magically vanish. We don’t know exactly where they went, but they are somewhere out of our sight.

So the lines aren’t really identical. They merely look like they are.

The gaps can’t magically vanish. The only thing we can do is push them out of our sight forever thereby creating an illusion that the two lines are identical.

They are not.

This “paradox” is known as Hilbert’s paradox of the Grand Hotel:
en.wikipedia.org/wiki/Hilbert%2 … rand_Hotel

I think Carleas mentioned it somewhere at the beginning of this thread (40-50 pages ago . . .)

Magnus, a paradox doesn’t mean that you’re right or wrong … have you disproved the paradox?

No.

So let’s look at the two gods argument again. A god is exactly half as omniscient as another god. Can that occur?

What does it mean to know half of everything if everything is infinite?

What about everything * 2?

Do you see why so many of us are debating you yet???

What’s everything * 2?

You mention contradictions frequently, but have an absolute blind spot to this very basic contradiction.

That’s why everyone else here is arguing against you.

That’s what you’re doing but you’re not recognizing it.

Allow me to repeat myself:

Whatever the quantity, if you subtract one from it, the quantity must change.

Suppose there is an infinite line of people somewhere in the universe and that YOU are one of the people waiting in it.

Suppose now that I take you by your hand, remove you from the line and place you somewhere outside of it.

The line is the same as it was before except that you’re no longer part of it. Noone joined the line, noone left it – except for you.

If you say that the number of people waiting in that line is the same as before, it either means that I didn’t really took you out of that line (that you’re still there) or that I did but that someone else joined it. Both are contradictions.

You never addressed this argument.

Magnus! If I subtracted you, you’d cease to exist. You would not be part of “another set”. You’d have no bearing on the infinity.

You aren’t following, Ecmandu.

I’ve addressed this argument before. Basically, the word “infinite” does not mean “the largest number possible” (let alone “everything”.) The word “infinite” means “endless”.

So “everything” by you! Doesn’t mean “endlesss”?

Keep going! I’m curious.

Not at all. And note that this isn’t merely “by me”.

To subtract does not mean to remove from existence. It means to remove from something where something can literally be anything.

Lol

So, you think that endless doesn’t imply everything, and that everything doesn’t imply endless.

Keep going.

“Everything” means “every element of some set” where “some set” can be literally any set.

E.g. “Everything you want” means “Every element of the set of things that you want”.

The set can be finite or infinite. It does not matter.

“Infinite” merely means “without an end”.

You can have a set made out of five infinite sets and the entire set would be more than any one of its five infinite sets.

You could ask “Which one of the sets do you want, Max?” And I could say “I want everything”. That would mean “Give me all five infinite sets, Sir”. In that particular context, “everything” would be representing five infinite sets. A finite number of sets each containing an infinite number of things.

Ok, that’s interesting.

So what if I say, “everything that exists throughout all existence, the cosmos”

And then a guy like you comes along and says, “every Tickle me Elmo that exists throughout existence an all the cosmos”

They are not equalities are they?

So why try to put them forward as such?

Especially if the universe is infinite (as it logically seems to be), there could be (and in fact logically seems to be) an infinity of apples, an infinity of oranges, and an infinity of pears.

The set of all three infinite sets is obviously greater than any one infinite subset.

Just basically speaking, this means an infinity of the finite. (The concept orange is finite) (Contradiction) or as mathematicians put it, “bound infinities”.

How do you bound an infinity (boundless)? (Contradiction)

Were you being sarcastic? Was that intentionally incoherent? Or??

“infinity of the finite”
“concept orange is finite”
“bound infinities”

None of those seem to have anything to do with the discussion.

I don’t get the gist of your argument. Are you saying there aren’t enough points to fill in all the gaps (I said points, not inches, but…), or that as soon as the gaps are out of sight, they stop being replaced?

If not enough points, how do you have not enough with an infinite amount?

Are you saying that we eventually run out of points to fill the gaps, and after the last point there’s nothing but gap? ← That would imply there’s an end to the series of point, and you know how that argument goes.

Magnus: “the concept of an orange is finite”

So what does infinite orange mean? Are you trying to tell me that you can have infinite oranges, but not single infinite orange? Well… if you can’t have a single orange and all those infinite oranges are equal as infinite orange, how can you have infinite oranges?

I’ve never joked, let alone joked sarcastically on ILP, even though in real life I do both abundantly.

Bound infinity has EVERYTHING to do with the discussion… it means infinity is a quantity

I’m saying there aren’t enough points. There aren’t enough points to fill the gaps that are within our sight without creating gaps out of our sight.

I am not.

We always have enough points to fill the gaps that are within our sight. But each time we fill the gaps that are within our sight, we create new gaps out of our sight.

Consider that in order to fill a gap, you have to remove a point elsewhere; and that when you remove a point, you create a gap in its place.

Here’s the infinite line with odd inches taken out:

( \circ \bullet \circ \bullet \circ \bullet \cdots )

Suppose you want to fill the first gap. How do you achieve that? By choosing an existing inch and moving it from its current place to the beginning of the line. You can pick any inch you want. There’s an infinite number of them. You can pick the first inch in the line. Let us do so. We pick the first inch in the line and move it to the beginning of the line. By doing so, we fill a gap but we also create a new gap. This is what follows:

( \bullet \circ \circ \bullet \circ \bullet \cdots )

We don’t get ( \bullet \bullet \circ \bullet \circ \bullet \cdots ). That would be creating new inches out of nowhere.

The interesting part is that you don’t have to pick an inch that is within your sight. You can pick an inch that is outside of your sight. You can pick the 100th inch or the 1,000th inch or the 1,000,000th one. In each case, you’d be creating a gap in its place. But because it’s out of your sight, it’s convenient to ignore it and pretend that the line no longer has any gaps.

It’s a trick. Something a magician would do. It’s definitely not logic.

Again Magnus,

Nobody has proven that there’s not a scatter set for the reals. Using your line logic, we’d have never ordered the rationals (the same logic applies)

In the absence of a scatter set, you can use my cheat.

1.) rational number
2.) uncounted number
3.) different rational number
4.) different uncounted number

Etc…

Even if we do prove that there’s no scatter set for the reals… you can still use my cheat.