Friday, 30 August 2013

What is Infinity?

 

Infinity ...
... it's not big ...
... it's not huge ...
... it's not tremendously large ...
... it's not extremely humongously enormous ...
... it's ...

Endless!

Infinity is not a real number

Infinity is not a real number, it is an idea. An idea of something without an end.
Infinity cannot be measured.
Even these faraway galaxies can't compete with infinity.

Here are some more properties:
Special Properties of Infinity
∞ + ∞ = ∞
-∞ + -∞ = -∞

∞ × ∞ = ∞
-∞ × -∞ = ∞
-∞ × ∞ = -∞

x + ∞ = ∞
x + (-∞) = -∞
x - ∞ = -∞
x - (-∞) = ∞

For x>0 :
x × ∞ = ∞
x × (-∞) = -∞
For x<0 :
x × ∞ = -∞
x × (-∞) = ∞

Undefined Operations

All of these are "undefined":
"Undefined" Operations
0 × ∞
0 × -∞
∞ + -∞
∞ - ∞
∞ / ∞
0
1

Example: Isn't ∞ / ∞ equal to 1?
No, because we really don't know how big infinity is, so we can't say that two infinities are the same. For example ∞ + ∞ = ∞, so
 =  ∞ + ∞ which would
mean that:
1 = 2




1 1
And that doesn't make sense!
I could have also made 1=3 and so on ... so we say that ∞ / ∞ is undefined.


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