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gib wrote:You are, once again, dismissing counter-examples.
By definition, if you have a bunch of things in one place (regardless of their number) and you subtract one thing, you get a smaller number of things. To say otherwise is to say that you didn't really perform the operation of subtraction, which is a logical contradiction.
Magnus Anderson wrote:gib wrote:You are, once again, dismissing counter-examples.
That's what you're doing but you're not recognizing it.
Allow me to repeat myself:By definition, if you have a bunch of things in one place (regardless of their number) and you subtract one thing, you get a smaller number of things. To say otherwise is to say that you didn't really perform the operation of subtraction, which is a logical contradiction.
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.
Ecmandu wrote: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.
Magnus Anderson wrote:Ecmandu wrote: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.
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".
Ecmandu wrote:So “everything” by you! Doesn’t mean “endlesss”?
Ecmandu wrote:If I subtracted you, you’d cease to exist. You would not be part of “another set”.
obsrvr524 wrote:Silhouette wrote:Actually I've known all this math since over half my life ago, and I have been regularly keeping up with advanced level maths to this day for fun - I actually really enjoy it.
And still can't get it right. I'm impressed.
Magnus Anderson wrote:Ecmandu wrote:So “everything” by you! Doesn’t mean “endlesss”?
Not at all. And note that this isn't merely "by me".
Magnus Anderson wrote:"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.
obsrvr524 wrote: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.
Ecmandu wrote: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)
Magnus Anderson wrote:gib wrote:Let's try this: imagine the scenario I described earlier, the one with two infinite parallel lines. For all intents and purposes, the same length. Now remove every odd point from one of the lines. Then move all remaining point into the spots left behind by the points you removed. According to you, the line with the points removed is now "shorter". But since we moved all points into the spots left empty from the points we removed, the lines are perfectly identical. It's as if we didn't remove any points at all. We're back to the initial state of the scenario. So here's your chance to shine. Help me understand how the lines are different now. Help me understand what it means that the line we removed points from is now "shorter".
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:
https://en.wikipedia.org/wiki/Hilbert%2 ... rand_Hotel
I think Carleas mentioned it somewhere at the beginning of this thread (40-50 pages ago . . .)
obsrvr524 wrote:Ecmandu wrote: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.
gib wrote: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?
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 Anderson wrote:gib wrote: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?
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.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.
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.
Aegean wrote:Still debating the theoretical meaning of '1'?
Existence happens between the theoretical absolutes of 1/0.
There is no 'one' in reality - nor a nil. It is a mental abstraction that can refer to anything the mind detaches from space/time and places within vague space/time borders.
'One' is an idea, representing an arbitrary moment/place.
Like all ideas it can be defined by the mind - synthesized, manipulated, redefined and redefined, combined, in ways that go beyond the real.
It is a linguistic representation of a mental abstraction, created by the translation of sensual stimuli.
0.9999 is not one...it is a movement towards an absolute that does not exist, and therefore can never be attained.
It represents the fluidity of existence, in relation to the mind's abstraction.
Aegean wrote:Still debating the theoretical meaning of '1'?
Existence happens between the theoretical absolutes of 1/0.
There is no 'one' in reality - nor a nil. It is a mental abstraction that can refer to anything the mind detaches from space/time and places within vague space/time borders.
'One' is an idea, representing an arbitrary moment/place.
Like all ideas it can be defined by the mind - synthesized, manipulated, redefined and redefined, combined, in ways that go beyond the real.
It is a linguistic representation of a mental abstraction, created by the translation of sensual stimuli.
0.9999 is not one...it is a movement towards an absolute that does not exist, and therefore can never be attained.
It represents the fluidity of existence, in relation to the mind's abstraction.
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