# Infinity * infinity

1. Feb 12, 2005

### chound

x + x = 2x
infinity + infinity = 2 infinity (or) infinity
x-x=0
infinity * infinity = square of infinity (or) infinity
:tongue:

2. Feb 12, 2005

### anti_crank

0 + 0 = 0.

Absolute nothingness + This thread = ....

3. Feb 26, 2005

### strid

have though alot about zeros and infinities... not a very high level maybe, but hey, I'm just 17....:)

about infinity + infinity = 2*infinity ?

see it like this.. in a 1cm line, there are infinite many points ...
in a 2cm line there is also infinite many points....

so if you have 2 1cm lines they will have infinite+infinite points, which is also infinite as the 2cm line also had infinite many points...

hope I wasnt confusing.....

and infinity * infinity = square of infinity ?

you have a line of any length with infinite many points.. say 1cm again
if you have four lines forming a square with, then, the area of 1cm^2 you will have infinite many points in the area......

so the lines of infinite many points, make a square with infinte * infinte many points in the square, which as said earlier his infinite..
so infinity * infinity = infinity..

I have some problem with infinity - infinity though...

I have infiinity.... I add another infinity and get.. infinity.. so If i subtract infinity now, I should get ack to my original number or?

so x+x-x = x or??
in case of infinty we get
x+x-x != x

weird.. but however.. its intresting stuf... have some other stuff i have thought of.. will post it another time.......

4. Feb 26, 2005

### Kerbox

since infinity is a proper subset of infinity+infinity, they can be put in one-to-one correspondence to eachother, and are then the same "degree" of infinity, am I right?

Last edited: Feb 26, 2005
5. Feb 26, 2005

### Hurkyl

Staff Emeritus

None of this makes any sense until you adopt some definitions... and then once you have, it's clear how things work.

6. Feb 26, 2005

### motai

Infinity is not a number, it is a mathematical concept. The reason it isn't a number is because for ever number at 'infinity' there is always a number that is greater than it. It doesn't make very much sense to use the concept of infinity as a mathematical operator.

Limits are the best way to show this correlation. If something is unbounded then it is useless to try to find a maximum number for Infinity.

7. Feb 26, 2005

### gravenewworld

x=.9999999...............
10x=9.999999.............

10x-x=9x=9.000000000000

x=1 thus 1=.99999999..............

1/3=.33333......
3(1/3)=3(.333333...........)
1=.999999999999999........

8. Feb 26, 2005

### gravenewworld

construct a right triangle, say a triangle with sides=1 and with hypotenuse sqrt(2). obviously sqrt(2)>1, how then can all the points on the side that has length of sqrt(2) be matched to all the points on the line that has length 1 like shown in the picture? this problem mystified Leibniz

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9. Feb 26, 2005

### strid

sorry, gravenewworld bu t i didnt umderstand......

10. Feb 26, 2005

### Kerbox

I believe he tried to illustrate that a line twice as long can be projected down on the first line as if two sides of a triangle, and you can match up each point on one line to each one on the other... therefore, they must have equal number of points?

11. Feb 26, 2005

### gravenewworld

Precisely kerbox

12. Feb 27, 2005

### Gokul43201

Staff Emeritus
$$\mathbb{Z} \subset \mathbb{R}$$, no ?

13. Feb 27, 2005

### derekmohammed

2x-x=0
2x=x
2=1 ????
-1=0 ????

How about them mathimatics!!

14. Feb 27, 2005

### strid

sorry to ruin your fun but your example doesnt work.. :tongue:

2x=x is ONLY true for 0 and infinity...
so when you have 2x=x and divide by x to get 2=1,
you actually divide by 0 or infinity. And as divison by 0 and infinity is undefined your conclusion is invalid...:)

just rememebered a quote by J.Baylock....
"If you want somone to hate you, explain to them, logically and politely, why they are wrong"

a funny thing of division of 0's can be demonstrated in this way (thought it myself, but someone else may have done it)

0*0=0
divide by 0 at both sides and you get
0=0/0

so is 0/0 equal to 0??? :grumpy:

nonono :tongue:

1*0=0
divide by 0 at both sides and you get
1=0/0
hihi
:rofl:

2*0=0
divide by 0 at both sides and you get
2=0/0
hihi
:rofl:

3*0=0
divide by 0 at both sides and you get
3=0/0
hihi
:rofl:

can cnotinue as long as I want... (or maybe not til infinity..)

15. Feb 28, 2005

### derekmohammed

I was refering to this... They give nonsence I give nonsence!

16. Mar 13, 2005

### jackle

I prefer to think of it like this:

ax=x => a=1 or x=0 or x=infinity.

so 2x=x => a=2 => x=0 or x=infinity.

17. Mar 13, 2005

### Hurkyl

Staff Emeritus
However, there is no number called "infinity", so "x = 0 or x = infinity" is equivalent to "x = 0"!

18. Mar 20, 2005

### Dirac

Infinity

Infinity is not a number.

Dirac.

19. Mar 20, 2005

### jackle

Does x always have to be a number in maths?

20. Mar 20, 2005

### arildno

You are using operations like multiplication and addition which are only defined on a set of numbers.