trial number one.

[bowmore]

this is where you fail. If k = infinity, then k-1 = k-2 = k = infinity. You'll never reach zero.

Prove it?  (on real objects)  

It is proven in mathematical set theory by Georg Cantor.

[Messenger]

this is where you fail. If k = infinity, then k-1 = k-2 = k = infinity. You'll never reach zero.

Prove it?  (on real objects)  

It is proven in mathematical set theory by Georg Cantor.

I said real objects not mathematics
Infinity In mathematics is different than in Physics, in Physics it is just an approximation

[bowmore]

Prove it?  (on real objects)  

It is proven in mathematical set theory by Georg Cantor.

I said real objects not mathematics
Infinity In mathematics is different than in Physics, in Physics it is just an approximation

You don't get to switch the tables here. You said you could prove you cannot have infinity in the real world.
Your argument was flawed because it disregarded mathematical properties of infinite numbers that are proven. That infinity in physics is just an approximation is what you should prove, not what can use as a premise.
It is a mistake on your part to assume I hold the contrary position. All I've claimed is that your proof doesn't work.

[Messenger]

You don't get to switch the tables here. You said you could prove you cannot have infinity in the real world.
Your argument was flawed because it disregarded mathematical properties of infinite numbers that are proven. That infinity in physics is just an approximation is what you should prove, not what can use as a premise.
It is a mistake on your part to assume I hold the contrary position. All I've claimed is that your proof doesn't work.

My proof works perfectly (it is called proof by contradictions)
You objected my proof by mathematical assumptions, which is out of context as we talk reality not hypothetically

Go back to my proof and try to refute it?

An infinite number of real objects is illogical (Logically contradicting i.e. a paradox and paradoxes don't exist

[bowmore]

All I've claimed is that your proof doesn't work.

My proof works perfectly (it is called proof by contradictions)

I know what a reductio ad absurdum is.

You objected my proof by mathematical assumptions, which is out of context as we talk reality not hypothetically

That doesn't mean you can simply disregard the mathematical properties of infinity.
That's like saying in reality 1 + 1 = 3, because the mathematical properties of the number 1 don't apply in reality.

If I have 10 apples and I remove 1 I'll be left with 9 apples.
If I have an infinite amount of apples and I remove 1 I still have an infinity of apples.

An infinite number of real objects is illogical (Logically contradicting i.e. a paradox and paradoxes don't exist

You only arrived at the paradox through faulty reasoning. The proof is invalid.

[Messenger]

That doesn't mean you can simply disregard the mathematical properties of infinity.
That's like saying in reality 1 + 1 = 3, because the mathematical properties of the number 1 don't apply in reality.

I don't disagree on the mathematical properties of infinity!
It is not like saying 1+1=3, because 1, 3 mathematical and physical properties are the same

If I have an infinite amount of apples and I remove 1 I still have an infinity of apples.

Can you prove that?

Here is the proof again (restated)
There exist N real apples (N can be anything)
Apples are edible (fact)
If I eat all of them I'll have No apples
if N=infinity N-1=N which means I did not eat any apple (Paradox)

[bowmore]

That doesn't mean you can simply disregard the mathematical properties of infinity.
That's like saying in reality 1 + 1 = 3, because the mathematical properties of the number 1 don't apply in reality.

I don't disagree on the mathematical properties of infinity!
It is not like saying 1+1=3, because 1, 3 mathematical and physical properties are the same

And it is up to you to prove that the same isn't true for infinity, since that is after all what you claim.

If I have an infinite amount of apples and I remove 1 I still have an infinity of apples.

Can you prove that?

Cantor's proved it for me.

Here is the proof again (restated)
There exist N real apples (N can be anything)
Apples are edible (fact)
If I eat all of them I'll have No apples
if N=infinity N-1=N which means I did not eat any apple (Paradox)

How does it mean you didn't eat an apple? That's just a non sequitur.
I bet if we study the contents of your stomach we'll find the pieces of the apple you've eaten.

Perhaps you should just count the apples you have left again. ( how do you practically establish the number of apples you have is infinite?)

Your proof seems to revolve around insisting that a real infinity should adopt the mathematical properties of finite numbers, whereas that is what you should prove, not assume.

[Messenger]

Cantor's proved it for me.

He didn't

Your proof seems to revolve around insisting that a real infinity should adopt the mathematical properties of finite numbers, whereas that is what you should prove, not assume.

I did not mention infinity in the first part, just some real apples, real apples follow physical rules (forget about mathematics here)
Then in the second part, we try to see if that real apples can match mathematics or not
We found that the assumption of infinity contradicts with agreed facts (which I ate the apples) i.e. a paradox
so the conclusion is that the assumption does not exist
Read about proof by contradictions

[bowmore]

Cantor's proved it for me.

He didn't

He proved it by showing it is possible to construct a bijection between a set containing an infinite number of elements (e.g. apples) and the same set containing one less.

Your proof seems to revolve around insisting that a real infinity should adopt the mathematical properties of finite numbers, whereas that is what you should prove, not assume.

I did not mention infinity in the first part, just some real apples, real apples follow physical rules (forget about mathematics here)

I suggest we don't forget mathematics as long as you haven't shown that infinity loses it's mathematical properties in reality.

Then in the second part, we try to see if that real apples can match mathematics or not
We found that the assumption of infinity contradicts with agreed facts (which I ate the apples) i.e. a paradox

Nope, you reached the paradox through faulty reasoning.

so the conclusion is that the assumption does not exist
Read about proof by contradictions

I told you I know what a reductio ad absurdum is. Yours just fails.

[Messenger]

He proved it by showing it is possible to construct a bijection between a set containing an infinite number of elements (e.g. apples) and the same set containing one less..

His proof is false and contradicting
He imagine that W is the first INTEGER which follows all the finite natural numbers, i.e., which can be called greater than any finite natural number.
which contradicts with the definition of infinite set

Nope, you reached the paradox through faulty reasoning.

Define it?

I told you I know what a reductio ad absurdum is. Yours just fails

You just assert

[bowmore]

His proof is false and contradicting
He imagine that W is the first INTEGER which follows all the finite natural numbers, i.e., which can be called greater than any finite natural number.
which contradicts with the definition of infinite set

Ok, that concludes it. You have no real mathematical background.
The set of all real numbers that are higher than 1 but smaller than two, is infinite. Let's call it A
2 is a real number that is greater than any element from A, and no real number exists that is lower than two, but greater than any element from A.
You see, you mix up order and cardinality. A set of infinite cardinality can have a upper limit that is not an element of that set. There is no contradiction there.

Nope, you reached the paradox through faulty reasoning.

Define it?

You assume without proof that infinity loses it's mathematical properties in reality.
Unlike most other mathematical concepts.

I told you I know what a reductio ad absurdum is. Yours just fails

You just assert

I did in this instance, as repeating my reasoning every time would get, well, repetitive.

[Messenger]

The set of all real numbers that are higher than 1 but smaller than two, is infinite. Let's call it A
2 is a real number that is greater than any element from A, and no real number exists that is lower than two, but greater than any element from A.
There is no contradiction there.

There is a contradiction because it is not a finite set!

You assume without proof that infinity loses it's mathematical properties in reality.

I proved it, and you failed to refute my proof

[SSY]

[quote="MessengerThere is a contradiction because it is not a finite set!
[/quote]

What is a contradiction? What is not a finite set? A?

[Messenger]

What is a contradiction? What is not a finite set? A?

Yes

[bowmore]

The set of all real numbers that are higher than 1 but smaller than two, is infinite. Let's call it A
2 is a real number that is greater than any element from A, and no real number exists that is lower than two, but greater than any element from A.
There is no contradiction there.

There is a contradiction because it is not a finite set!

Again you prove your lack of a sufficient mathematical background.

Of course you will back up your claim and give me a number (let's represent it by m) so that m is a real number, m < 2, and for all n for which (n > 1 and n<2) : m > n

But you may as well not bother since whatever m you choose I'll nominate n=m+(2-m)/2