Infinity: Square of Infinity + 2 Infinity

[chound]

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

 

[anti_crank]

0 + 0 = 0.

Absolute nothingness + This thread = ...

 

[strid]

have though a lot 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 infinite * infinite 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 interesting stuf... have some other stuff i have thought of.. will post it another time...

 

[Kerbox]

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

 

[Hurkyl]

Head... hurting...

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

 

[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.

 

[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...

 

[gravenewworld]

also how about this one:
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

 

[strid]

sorry, gravenewworld bu t i didnt umderstand...

 

[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?

 

[gravenewworld]

Precisely kerbox

 

[Gokul43201]

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

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

 

[derekmohammed]

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

How about them mathimatics!

 

[strid]

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

How about them mathimatics!

sorry to ruin your fun but your example doesn't work..

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 someone 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?

nonono

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


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


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


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

 

[derekmohammed]

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

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

 

[jackle]

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

How about them mathimatics!

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.

 

[Hurkyl]

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

 

[Dirac]

Infinity

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

Infinity is not a number.

Dirac.

 

[jackle]

Does x always have to be a number in maths?

 

[arildno]

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

 

[jackle]

I think someone posted something about "extended reals" somewhere but I can't find the link and I got no matches on my web search. Can you tell me anything about that, or is it bad maths?

 

[Hurkyl]

The extended reals are to the reals as [0, 1] is to (0, 1) -- the extended reals complete the real numbers as a topological space by adding two "endpoints" (+∞ and -∞). This topological space cleans up a great deal of calculus. For example, you no longer need to have a separate definition for when a limit diverges to +∞.

However, the key point to note is that the extended reals aren't an arithmetic structure -- we can extend the functions +, -, *, and / to take (some) infinite values, but this extension is via continuity as opposed to any arithmetic meaning.

Another example of an extension via continuity is extending the function (x-1)/(1-x) to equal -1 at x=1, or extending the function (sin x)/x to equal 1 at x=0.

These extensions of +, -, *, and / now need to be thought of merely as functions -- it is generally wrong to try and treat them as arithmetic operations when they take on infinite values.


As an example, the function f(x) = 2x - x cannot have +∞ in its domain, because if we try to evaluate, we run into (+∞) - (+∞), which is undefined.

Why is it undefined? Because no matter what value we assign to it, it would render the - operation discontinuous there. For example, consider:

$$(+\infty) - (+\infty) = (\lim_{x \rightarrow \infty} x+1) - (\lim_{x \rightarrow \infty} x) = \lim_{x \rightarrow \infty} ((x + 1) - x) = 1$$
$$(+\infty) - (+\infty) = (\lim_{x \rightarrow \infty} x) - (\lim_{x \rightarrow \infty} x+1) = \lim_{x \rightarrow \infty} (x - (x + 1)) = -1$$

If - was continuous at (+∞, +∞), then both of these statements would be true -- the first equality by definition of continuity, and the rest as properties of limits.

(This is very closely related to the concept of an "indeterminate form")

 

[Hurkyl]

Whoops, I made a slight mistake. What continuity says here is:

$$\lim_{(x, y) \rightarrow (a, b)} (f(x) - g(y)) = \left( \lim_{(x, y) \rightarrow (a, b)} f(x) \right) - \left( \lim_{(x, y) \rightarrow (a, b)} g(y) \right)$$

when the appropriate conditions are satisfied (existence, domains, etc). But, you can still make that proof by contradiction.

 

[Quarkycharm]

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

How about them mathimatics!

I'd rather think of it as only x=0, as "infinity" isn't a well defined number or digit..

 

[phoenixthoth]

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

Do you mean:
for all x, x+x=2x, THEREFORE ∞+∞=2∞=∞?

What does the minus mean in x-x when x=∞?

Are these infinities the extended real numbers or infinite sets or something else?