Infinite = 1

[arkain101]

I think infinity is misunderstood.

 

Infinite means forever. I think that in order to understand infinity you have to imagine no time, and close your eyes and think, all I can do is change.

[T0M]

That's not science. Science does not accept such things as fact without proof and your claim does not add up. If all infinities are equal then why does math differentiate between a countably infinite set and an uncountably infinite set?

I wasn't familiarized with so many terms in your reply (lack of formal education), so I had to do a bit of research.

So thank you for making me do a research, and nice website by the way. I'll first share my research with everybody, and afterwards, once I cleared my ignorance about your terms I'll reply.

 

So...

 

Set: Is a finite or infinite collection of objects in which order has no significance.

 

Countably set: A set which is either finite or denumerable.

 

Denumerable set: A set is denumerable iff (that means only if) it is equipollent to the finite ordinal numbers.

 

Ordinal number: An ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc.

 

Well now...

 

Uncountably infinite set: An infinite set, such as the real numbers, which is not countably infinite.

 

Countably infinite set: Any set which can be put in a one-to-one correspondence (bijection) with the natural numbers (or integers) so that a prescription can be given for identifying its members one at a time.

 

Bijection: A transformation which is one-to-one (injection) and onto (surjection).

 

For these three terms (injection, surjection and bijection) I'll use some graphics from that website for it will be easier to understand. It's just about making reference from one set (of objects, numbers) to another. In this website's words: Let f be a function defined on a set A and taking values in a set B.

 

So...

 

Injection:

 

Surjection:

 

Then...

 

Bijection:

 

So, now that we have all understood these terms, see how a Countably set is either finite (opposite of infinite) or denumerable (equipollent to the finite ordinal numbers). So, to begin, a Countably set is NOT infinite. Let's not get confused by the terminology used sometimes.

A Countably infinite set is just a set bijectable with the natural numbers. Of course it's "countable" for natural numbers are "countable". But as they are infinite, they are not really countable, aren't they?

So that has nothing to do really with the meaning of the concept Infinite.

So...

 

Would you claim the set of real numbers is the same size as the set of integers? Can you prove it?

Yes. I can prove it, why not.

Let's call A the "size" of the "set of real numbers", and B the "size" of the "set of integers". ∞ will be Infinite, as usual.

 

A = ∞

 

B = ∞

 

∞ = ∞

 

So...

 

A = B

 

BTW, you might want to take a look at the rules here. Number 4 in particular states, "Statements like "I just know that this is the way it is" are considered ignorant and might be deleted." Can you prove your claim or are you just proffering a theory?

Thank you, I don't usually read rules because my own rules about my own behaviour are normally more strict and appropiate, but I'll give them a look.

Did I give you the impression that I was saying "I just know that this is the way it is"? Like mmm... religion? Then I'm sorry, it wasn't my intention.

And then... aren't you trying to prove me wrong? Do you have proves or you just know that this is not the way it is?

I'm willing to prove that my theory is less unprovable than any other. Because that's the closest we'll ever get to prove an explaination of the concept of infinite. With today's languages.

So shoot.

 

T0M

[T0M]

I think infinity is misunderstood.

 

Infinite means forever. I think that in order to understand infinity you have to imagine no time, and close your eyes and think, all I can do is change.

Well, forever implies time as a term, so that would be confuse for time itself is not understood and misunderstood. Let's not even mention time.

Besides that, you're right, all that can be done is "change", and the only way to walk that last mile in getting close to understand it is by closing your eyes and thinking.

 

T0M

[C1ay]

And then... aren't you trying to prove me wrong? Do you have proves or you just know that this is not the way it is?

I'm willing to prove that my theory is less unprovable than any other. Because that's the closest we'll ever get to prove an explaination of the concept of infinite. With today's languages.

So shoot.

Nope. I don't need to prove you wrong. You've made a claim and it's your burden to support it, not others to disprove it. Here's something to think about though. You've claimed that the infinity approached by the enumeration of real numbers is the same as the one approached by the enumeration of integers. It is implicit that these enumerations are then equal such that we could make a one-to-one mapping of the sets' members. This is easily disproven by the fact that the reals are uncountably infinite and the integers are countably infinite. Their enumeration does not approach the same value of infinity.

[T0M]

... You've claimed that the infinity approached by the enumeration of real numbers is the same as the one approached by the enumeration of integers...

I haven't claimed that the infinity is approached by any enumeration. Infinite can't be approached. An end can be approached, but not the infinite, which has no end.

 

It is implicit that these enumerations are then equal such that we could make a one-to-one mapping of the sets' members. This is easily disproven by the fact that the reals are uncountably infinite and the integers are countably infinite. Their enumeration does not approach the same value of infinity.

There's no value of intinite to approach to. There's no point on enumerating to infinity. If you want to go to infinite, don't move from 0. That's more infinite than making one step out of it.

 

I have a question for you:

What is the first of the Real numbers?

(if it is cero, not that one, the next one)

 

T0M

[C1ay]

Infinite can't be approached. An end can be approached, but not the infinite, which has no end.

Another unsupported claim. Now you imply that all limits evaluated as x approaches infinity are invalid because you can't approach infinity. Produce some proof or this thread's headed for the Strange Claims Forum.

[T0M]

I have a question for you:

What is the first of the Real numbers?

(if it is cero, not that one, the next one)

Please answer my question, I have a point but I need to clear this up first.

 

T0M

[C1ay]

[/center]

Please answer my question, I have a point but I need to clear this up first.

 

T0M

I don't believe there is a first number. The reals include all numbers, positive and negative, so they are unbounded.

[T0M]

I don't believe there is a first number. The reals include all numbers, positive and negative, so they are unbounded.

The first of the positive Real numbers is 1/∞, that's pretty obvious isn't it?

 

T0M

[C1ay]

The first of the positive Real numbers is 1/∞, that's pretty obvious isn't it?

 

T0M

No

[T0M]

The first of the positive Real numbers is 1/∞, that's pretty obvious isn't it?

No

Don't you agree? I think that that must already be a fact in Maths.

I'll start a thread asking.

 

T0M

[C1ay]

Don't you agree? I think that that must already be a fact in Maths.

I'll start a thread asking.

 

T0M

Actually the limit of 1/x as x appproaches infinity is 0. I would think that 0 is the middle of the number line that runs from -infinity to +infinity.

[T0M]

Actually the limit of 1/x as x appproaches infinity is 0. I would think that 0 is the middle of the number line that runs from -infinity to +infinity.

Again, that's rounding!

And yes! Between infinite and -infinite is 0.

So finally you're agreeing that there's only one infinite and not several as you said before!

 

T0M

[jettlarue]

Isnt it that x=infinity is just a possibility but it can never exist because x is an interger and infinity is a state of beng because you can never be halfway to infinity or past it. It is just a possibility that is impossible with our current physics.

[T0M]

Isnt it that x=infinity is just a possibility but it can never exist because x is an interger and infinity is a state of beng because you can never be halfway to infinity or past it. It is just a possibility that is impossible with our current physics.

x is not an integer.

Of course there's no half-way to infinity or past it.

And possibilities are not impossible. As impossibilities are not possible.

 

T0M

[my brain hurts]

Again, that's rounding!

And yes! Between infinite and -infinite is 0.

So finally you're agreeing that there's only one infinite and not several as you said before!

 

T0M

 

No matter how much you'd like them to, transfinite numbers simply don't obey mathematical operations the same way as finite numbers. Your attempt to insert infinity (and there most certainly is more than one) into a simple fraction and say "See! I've proved it!" is about as convincing as claiming to cure cancer by shaking a dead chicken over the patient's head.

 

In the scheme of things, the first infinity, Aleph-null, is no more than small potatoes.

[C1ay]

Again, that's rounding!

And yes! Between infinite and -infinite is 0.

So finally you're agreeing that there's only one infinite and not several as you said before!

 

T0M

Nope. I just mentioned two of them. Mathematically you can form an infinite number of infinite sets between any two points. This thread's headed for strange claims too.