What is Infinity?

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

Endless!

Infinity has no end

Infinity is the idea of something that has no end.

In our world we don't have anything like it. So we imagine traveling on and on, trying hard to get there, but that is not actually infinity.

So don't think like that (it just hurts your brain!). Just think "endless", or "boundless".

If there is no reason something should stop, then it is infinite.

Infinity does not grow

Infinity is not "getting larger", it is already fully formed.

Sometimes people (including me) say it "goes on and on" which sounds like it is growing somehow. But infinity does not do anything, it just is.

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.

Infinity is Simple

Yes! It is actually simpler than things which do have an end. Because when something has an end, we have to define where that end is.

Example: in Geometry a "Line" has infinite length ... it goes in both directions without an end. If it has one end it is called a Ray, and if it has two ends it is called a Line Segment, but that needs extra information to define where the ends are.
More Examples:
{1, 2, 3, ...}	The sequence of natural numbers never ends, and is infinite.
1/3	OK, 1/3 is a finite number (it is not infinite). But written as a decimal number the digit 3 repeats forever (we say "0.3 repeating"): 0.3333333... (etc) There's no reason why the 3s should ever stop: they repeat infinitely.
0.999...	So, when we see a number like "0.999..." (i.e. a decimal number with an infinite series of 9s), there is no end to the number of 9s. You cannot say "but what happens if it ends in an 8?", because it simply does not end. (This is why 0.999... equals 1).
AAAA...	An infinite series of "A"s followed by a "B" would NEVER have a "B".
	There are infinite points in a line. Even a short line segment has infinite points.

 Big Numbers

There are some really impressively big numbers.

A Googol is 1 followed by one hundred zeros (10¹⁰⁰) :

10,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000

A Googol is already bigger than the number of elementary particles in the known Universe, but then there is the Googolplex. It is 1 followed by Googol zeros. I can't even write down the number, because there is not enough matter in the universe to form all the zeros:

10,000,000,000,000,000,000,000,000,000,000,000,000, ... (Googol number of Zeros)

And there are even larger numbers that need to use "Power Towers" to write them down.

For example, a Googolplex can be written as this power tower: 

That is ten to the power of (10 to the power of 100),

But imagine an even bigger number like (which is a Googolplexian).

And we can easily create much larger numbers than those!

Finite

All of these numbers are "finite", we could eventually "get there".

But none of these numbers are even close to infinity. Because they are finite, and infinity is ... not finite!

Using Infinity

We can sometimes use infinity like it is a number, but infinity does not behave like a real number.

To help you understand, think "endless" whenever you see the infinity symbol "∞":

For example: ∞ + 1 = ∞

Which says that infinity plus one is still equal to infinity.

When something is already endless, we can add 1 and it is still endless.

The most important thing about infinity is that:

-∞ < x < ∞ Where x is a real number

Which is mathematical shorthand for
"negative infinity is less than any real number,
and infinity is greater than any real number"

Here are some more properties:

Special Properties of Infinity

∞ + ∞ = ∞

-∞ + -∞ = -∞

∞ × ∞ = ∞

-∞ × -∞ = ∞

-∞ × ∞ = -∞

x + ∞ = ∞

x + (-∞) = -∞

x - ∞ = -∞

x - (-∞) = ∞

For x>0 :

x × ∞ = ∞

x × (-∞) = -∞

For x<0 :="" o:p="">

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 means 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.

Infinite Sets

If you continue to study this subject you will find discussions about infinite sets, and the idea ofdifferent sizes of infinity.

That subject has special names like Aleph-null (how many Natural Numbers), Aleph-one and so on, which are used to measure the sizes of sets.

For example, there are infinitely many whole numbers {0,1,2,3,4,...},

But there are more real numbers (such as 12.308 or 1.1111115) because there are infinitely many possible variations after the decimal place as well.

But that is an advanced topic, and goes beyond the simple concept of infinity we discuss here.

Conclusion

Infinity is a simple idea: "endless". Most things we know have an end, but infinity does not.

Check Your LPG Gas Cylinder Expiry Date

LPG gas is the most used cooking fuel in India and many other countries. Not only does it make your mother's kitchen work convenient, it is also a live bomb sitting just next to her almost all the time.

Did you know that there is an expiry date (physical life) for LPG cylinders? Expired Cylinders are not safe for use and can cause lethal accidents.

Here is how you can check the expiry date of LPG cylinders:
On one of three side stems of the cylinder, the expiry date is coded alpha numerically which starts with A, B, C or D followed by a two digit number. e.g. D06.

The alphabets stand for quarters -

• A for March (First Qtr),
• B for June (Second Qtr),
• C for Sept (Third Qtr),
• D for December (Fourth Qtr).

The digits stand for the year till it is valid. Hence D-06 would mean December quarter of 2006.

(This means Your cylinder expires on: December 2006)

The most imminent danger is to your mother, wife, sister... Kindly pass this on, for creating awareness.

So next time your delivery boy comes with a re-fill cylinder, make sure you check the expiry date. Many local LPG re-fillers even conceal the date, usually by pasting some sticker over it. So please be extra careful while checking

If you get a cylinder post expiry date, please return it back immediately, they are highly prone to leaking or bursting causing serious injuries and can even take life.

Although finding the expiry date is not hard at all if you know the trick, an average common man would almost never be able to decipher it. I wonder how difficult it is for the LPG companies to write something like "exp: Dec-2006" instead of such an alien code. Or may be they too want to conceal it? Any way, here's an easy way - Just enter your code in the box below to get the correct expiry date.

Multiply Up to 20X20 In Your Head

In just FIVE minutes you should learn to quickly multiply up to 20x20 in your head.  With this trick, you will be able to multiply any two numbers from 11 to 19 in your head quickly, without the use of a calculator.

I will assume that you know your multiplication table reasonably well up to 10x10.

Try this:

1.      Take 15 x 13 for an example.

2.      Always place the larger number of the two on top in your mind.

3.      Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.

4.      First add 15 + 3 = 18

5.      Add a zero behind it (multiply by 10) to get 180.

6.      Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15)

7.      Add 180 + 15 = 195.

The 11 Rule

You likely all know the 10 rule (to multiply by 10, just add a 0 behind the number) but do you know the 11 rule? It is as easy! You should be able to do this one in you head for any two digit number. Practice it on paper first!

To multiply any two digit number by 11:

1.      For this example we will use 54.

2.      Separate the two digits in you mind (5__4).

3.      Notice the hole between them!

4.      Add the 5 and the 4 together (5+4=9)

5.      Put the resulting 9 in the hole 594. That's it! 11 x 54=594

The only thing tricky to remember is that if the result of the addition is greater than 9, you only put the "ones" digit in the hole and carry the "tens" digit from the addition. For example 11 x 57 ... 5__7 ... 5+7=12 ... put the 2 in the hole and add the 1 from the 12 to the 5 in to get 6 for a result of 627 ... 11 x 57 = 627

Finger Math: 9X Rule

To multiply by 9,try this:

(1)   Spread your two hands out and place them on a desk or table in front of you.

(2)   To multiply by 3, fold down the 3rd finger from the left. To multiply by 4, it would be the 4th finger and so on.

(3)   the answer is 27 ... READ it from the two fingers on the left of the folded down finger and the 7 fingers on the right of it.

This works for anything up to 9x10!

Square a 2 Digit Number Ending in 5

For this example we will use 25

(1)   Take the "tens" part of the number (the 2 and add 1)=3

(2)   Multiply the original "tens" part of the number by the new number (2x3)

(3)   Take the result (2x3=6) and put 25 behind it. Result the answer 625.

Try a few more 75 squared ... = 7x8=56 ... put 25 behind it is 5625.

55 squared = 5x6=30 ... put 25 behind it ... is 3025. Another easy one! Practice it on paper first!

Square 2 Digit Number: UP-DOWN Method

Square a 2 Digit Number, for this example 37:

(1)   Look for the nearest 10 boundary

(2)   In this case up 3 from 37 to 40.

(3)   Since you went UP 3 to 40 go DOWN 3 from 37 to 34.

(4)   Now mentally multiply 34x40

(5)   The way I do it is 34x10=340;

(6)   Double it mentally to 680

(7)   Double it again mentally to 1360

(8)   This 1360 is the FIRST interim answer.

(9)   37 is "3" away from the 10 boundary 40.

(10)           Square this "3" distance from 10 boundary.

(11)           3x3=9 which is the SECOND interim answer.

(12)           Add the two interim answers to get the final answer.

(13)           Answer: 1360 + 9 = 1369

Multiply By 4

To quickly multiply by four, double the number and then double it again.

Often this can be done in your head.

Multiply By 5

To quickly multiply by 5, divide the number in two and then multiply it by 10.  Often this can be done quickly in your head.

The 11 Rule Expanded

You can directly write down the answer to any number multiplied by 11.

(1)   Take for example the number 51236 X 11.

(2)   First, write down the number with a zero in front of it.

051236

The zero is necessary so that the rules are simpler.

(1)   Draw a line under the number.

(2)   Bear with me on this one. It is simple if you work through it slowly. To do this, all you have to do this is "Add the neighbor". Look at the 6 in the "units" position of the number. Since there is no number to the right of it, you can't add to its "neighbor" so just write down 6 below the 6 in the units col.

(3)   For the "tens" place, add the 3 to the its "neighbor" (the 6). Write the answer: 9 below the 3.

(4)   For the "hundreds" place, add the 2 to the its "neighbor" (the 3). Write the answer: 5 below the 2.

(5)   For the "thousands" place, add the 1 to the its "neighbor" (the 2). Write the answer: 3 below the 1.

(6)   For the "ten-thousands" place, add the 5 to the its "neighbor" (the 1). Write the answer: 6 below the 5.

(7)   For the "hundred-thousands" place, add the 0 to the its "neighbor" (the 5). Write the answer: 5 below the 0.

That's it ... 11 X 051236 = 563596