Is there really a number larger than infinity?

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Grasshopper27

Banned
Sep 11, 2002
7,013
1
0
Originally posted by: SagaLore
Originally posted by: hdeck
Originally posted by: ElFenix
.999... !=0

amen to that.

*edit* it's also fun to realize that a straight line is actually just a circle with radius infinity. :)

But if that's true, if you travel the infinite radius it must at some point come to a complete loop :Q

It will, after an infinite amount of time. :D
 

CallTheFBI

Banned
Jan 22, 2003
761
0
0
Originally posted by: notfred
f(x) = x^2;
g(x) = x^4;

the limit as x->infinity of f(x) is infinity. The limit as x->infinity of g(x) is infinity. However, note that g(x) is always greater than f(x), so how can they both have the same limit?

g(x) approaches a larger infinity than f(x) does. This can happen because infinity isn't a number, but more of an abstract concept of open-endedness.

What? A larger infinity? I just thought that one of them gets there a LOT faster but they are both the same infinity. Anyways, I've been flipping through my textbook to no avail, it doesn't say anything about one infinity being larger than another.

 

notfred

Lifer
Feb 12, 2001
38,241
4
0
Originally posted by: CallTheFBI
Originally posted by: notfred
f(x) = x^2;
g(x) = x^4;

the limit as x->infinity of f(x) is infinity. The limit as x->infinity of g(x) is infinity. However, note that g(x) is always greater than f(x), so how can they both have the same limit?

g(x) approaches a larger infinity than f(x) does. This can happen because infinity isn't a number, but more of an abstract concept of open-endedness.

What? A larger infinity? I just thought that one of them gets there a LOT faster but they are both the same infinity. Anyways, I've been flipping through my textbook to no avail, it doesn't say anything about one infinity being larger than another.

Are you denying that x^4 is always greater than x^2? If x^4 gets to infinity faster than x^2 does, can you tell me the value of x when x^4 equals infinity, and show that x^2=infinity occurs at a higher x value?

It's probably in your calculus book somewhere :)
 

dxkj

Lifer
Feb 17, 2001
11,772
2
81
But if that's true, if you travel the infinite radius it must at some point come to a complete loop :Q


see, a straight line through space really is curved!
 

CallTheFBI

Banned
Jan 22, 2003
761
0
0
Originally posted by: notfred
Originally posted by: CallTheFBI
Originally posted by: notfred
f(x) = x^2;
g(x) = x^4;

the limit as x->infinity of f(x) is infinity. The limit as x->infinity of g(x) is infinity. However, note that g(x) is always greater than f(x), so how can they both have the same limit?

g(x) approaches a larger infinity than f(x) does. This can happen because infinity isn't a number, but more of an abstract concept of open-endedness.

What? A larger infinity? I just thought that one of them gets there a LOT faster but they are both the same infinity. Anyways, I've been flipping through my textbook to no avail, it doesn't say anything about one infinity being larger than another.

Are you denying that x^4 is always greater than x^2? If x^4 gets to infinity faster than x^2 does, can you tell me the value of x when x^4 equals infinity, and show that x^2=infinity occurs at a higher x value?

It's probably in your calculus book somewhere :)

Yes I am denying that X^4 is always greater than X^2. For the values of 0, 1 and infinity that statement is false. Not to mention the values between -1 and 1.

 

DeafeningSilence

Golden Member
Jul 2, 2002
1,874
1
0
Your teacher was referring to the Continuum Hypothesis. It involves different levels of infinity. The whole topic really is fascinating -- I did my senior math seminar research project on it last year.

Here's a pretty good explanation.

Here's my super-simplified one sentence explanation: If you listed all the possible decimal numbers between 0 and 1, and assigned each of them a counting number between 1 and Infinity, you would find that there are decimal numbers that you missed --> thus, there exists a 'number' greater than infinity. (Ok, so it was a run-on sentence. :) )
 

HendrixFan

Diamond Member
Oct 18, 2001
4,646
0
71
Originally posted by: notfred
Originally posted by: CallTheFBI
Originally posted by: notfred
f(x) = x^2;
g(x) = x^4;

the limit as x->infinity of f(x) is infinity. The limit as x->infinity of g(x) is infinity. However, note that g(x) is always greater than f(x), so how can they both have the same limit?

g(x) approaches a larger infinity than f(x) does. This can happen because infinity isn't a number, but more of an abstract concept of open-endedness.

What? A larger infinity? I just thought that one of them gets there a LOT faster but they are both the same infinity. Anyways, I've been flipping through my textbook to no avail, it doesn't say anything about one infinity being larger than another.

Are you denying that x^4 is always greater than x^2? If x^4 gets to infinity faster than x^2 does, can you tell me the value of x when x^4 equals infinity, and show that x^2=infinity occurs at a higher x value?

It's probably in your calculus book somewhere :)

notfred is right. Both numbers are infinitely large, but they expand at different rates.

Edit: you cant plug in 0 or 1 into the equation, or 2 for that matter. 2^2 =4 and 2^4 =16. Infinity ^2 = infinity and infinity ^4 = infinity.
 

CallTheFBI

Banned
Jan 22, 2003
761
0
0
Originally posted by: DeafeningSilence
Your teacher was referring to the Continuum Hypothesis. It involves different levels of infinity. The whole topic really is fascinating -- I did my senior math seminar research project on it last year.

Here's a pretty good explanation.

Here's my super-simplified one sentence explanation: If you listed all the possible decimal numbers between 0 and 1, and assigned each of them a counting number between 1 and Infinity, you would find that there are decimal numbers that you missed --> thus, there exists a 'number' greater than infinity. (Ok, so it was a run-on sentence. :) )



The Continuum Hypothesis states simply that aleph1= c

Ok, there is the c she was talking about. Now we are getting somewhere.
 

notfred

Lifer
Feb 12, 2001
38,241
4
0
Originally posted by: CallTheFBI
Originally posted by: notfred
Originally posted by: CallTheFBI
Originally posted by: notfred
f(x) = x^2;
g(x) = x^4;

the limit as x->infinity of f(x) is infinity. The limit as x->infinity of g(x) is infinity. However, note that g(x) is always greater than f(x), so how can they both have the same limit?

g(x) approaches a larger infinity than f(x) does. This can happen because infinity isn't a number, but more of an abstract concept of open-endedness.

What? A larger infinity? I just thought that one of them gets there a LOT faster but they are both the same infinity. Anyways, I've been flipping through my textbook to no avail, it doesn't say anything about one infinity being larger than another.

Are you denying that x^4 is always greater than x^2? If x^4 gets to infinity faster than x^2 does, can you tell me the value of x when x^4 equals infinity, and show that x^2=infinity occurs at a higher x value?

It's probably in your calculus book somewhere :)

Yes I am denying that X^4 is always greater than X^2. For the values of 0, 1 and infinity that statement is false. Not to mention the values between -1 and 1.

ok, not all x values, but x values anywhere remotely close to infinity, meaning: they have an absolute value greater than 1.

Infinity is not a number, you cannot compute infinity to the 4th power, or infinity squared. Like I said, show me the x value when x^4 = infinity, or when x^2 equals infinity, and show that x^4 equals infinity before x^2 does.
 

CallTheFBI

Banned
Jan 22, 2003
761
0
0
Originally posted by: notfred
Originally posted by: CallTheFBI
Originally posted by: notfred
Originally posted by: CallTheFBI
Originally posted by: notfred
f(x) = x^2;
g(x) = x^4;

the limit as x->infinity of f(x) is infinity. The limit as x->infinity of g(x) is infinity. However, note that g(x) is always greater than f(x), so how can they both have the same limit?

g(x) approaches a larger infinity than f(x) does. This can happen because infinity isn't a number, but more of an abstract concept of open-endedness.

What? A larger infinity? I just thought that one of them gets there a LOT faster but they are both the same infinity. Anyways, I've been flipping through my textbook to no avail, it doesn't say anything about one infinity being larger than another.

Are you denying that x^4 is always greater than x^2? If x^4 gets to infinity faster than x^2 does, can you tell me the value of x when x^4 equals infinity, and show that x^2=infinity occurs at a higher x value?

It's probably in your calculus book somewhere :)

Yes I am denying that X^4 is always greater than X^2. For the values of 0, 1 and infinity that statement is false. Not to mention the values between -1 and 1.

ok, not all x values, but x values anywhere remotely close to infinity, meaning: they have an absolute value greater than 1.

Infinity is not a number, you cannot compute infinity to the 4th power, or infinity squared. Like I said, show me the x value when x^4 = infinity, or when x^2 equals infinity, and show that x^4 equals infinity before x^2 does.

You may be right, my memory on this topic is a bit hazy since all I have been doing for the past couple weeks is advanced integration techniques. However, my teacher said that weather or not infinity is a number is debateable. In other words some mathemeticians will tell you that it is quite alright to perform operations on infinity as if it were a regular number. Other mathematicians will tell you that infinity does not exist outside a limit. For instance you can't just say x = infinity you have to say the limit as x goes to infinity. The authors of my Calculus text are in the school of thought that it has to be in a limit at all times, looking through my text I never see infinity by itself. At least that is what I believe I understood from what she told us. When she was doing a limit on the board one time she did operations on infinity and said that the authors of our texts would roll over in their grave.

The makers of the TI-89 however let you perform operations on infinity outside a limit to your hearts intent.
 

Kev

Lifer
Dec 17, 2001
16,367
4
81
Originally posted by: notfred
f(x) = x^2;
g(x) = x^4;

the limit as x->infinity of f(x) is infinity. The limit as x->infinity of g(x) is infinity. However, note that g(x) is always greater than f(x), so how can they both have the same limit?

g(x) approaches a larger infinity than f(x) does. This can happen because infinity isn't a number, but more of an abstract concept of open-endedness.

This is a contradiction, how could one infinity be larger than another if infinity really isn't a number? How would you quantify it? It's impossible.

The simple answer to this is to look at infinity as a concept. It's not really a number, so you can't have anything greater than it.
 

Toasthead

Diamond Member
Aug 27, 2001
6,621
0
0
Infinity isnt a number. Its an abstract concept. Therefore nothing can be bigger than it. Infinity includes all known numbers so it would be impossible to add anything to it.

 

Azraele

Elite Member
Nov 5, 2000
16,524
29
91
Originally posted by: Toasthead
Infinity isnt a number. Its an abstract concept. Therefore nothing can be bigger than it. Infinity includes all known numbers so it would be impossible to add anything to it.
What Toast said. :)

 

CallTheFBI

Banned
Jan 22, 2003
761
0
0
Originally posted by: Toasthead
Infinity isnt a number. Its an abstract concept. Therefore nothing can be bigger than it. Infinity includes all known numbers so it would be impossible to add anything to it.


WRONG! Click the link and read.
 

everman

Lifer
Nov 5, 2002
11,288
1
0
You can have infinite sets that can be said to be larger than other infinite sets.
Ex: all integers from 1,2,3 etc +1 to each infinitly. The infinite set of all decimals is larger in that it includes 1 and all decimals in between 1 and 2, 2 and 3, etc.

 

BDawg

Lifer
Oct 31, 2000
11,631
2
0
Originally posted by: guapo337
Originally posted by: iamwiz82
Originally posted by: CallTheFBI
Originally posted by: BDawg
Infinity + 1 is larger than infinity.

No, it actually isn't. Infinity + 1 = Infinity. Infinity - Infinity is actually an inderterminate form though which means it could equal anything. You learn about this when you study limits in Calculus 1.


Personally, i think you are Jerboy under a different name.

you're not the only one. let's make a "callthefbi list"

:D

I bet his password is n0fr33sk00llunch4u