My Story Page 28

Infinity

Posting to third eye bloglet - My Story Page 28 - Infinity : 26th January, 2007.

The date-wise archives of third eye bloglet - My Story: My Date with My Body - about eyes, mind, sex, science, and society turned into web pages. My Story Page 28 makes a real interesting reading:

What is infinity?

What do we mean when we say something is at an infinite distance from a given point in question?

Do we mean to say endless?

What does the term 'endless' mean?

You go on going and going and going, and you will never reach it.

Is it possible?

Is universe infinite?

We know it is not. It is finite, and that's why and how it is going on expanding with the passage of time (?)!

If we go on going and going and going (somehow!), we'll reach the end of the universe.

What if we take one more step out?

Can we?

Why not? We have our free will with us!

So, what if we take one more step out?

We'll come in, where we started from!

This is what infinity is.

∞ = 0

Exactly zero!

If it is, it must satisfy all the basic mathematical operations.

Let's come to them - the basic mathematical operations with zero!

1. 0/anything = 0

2. Anything/0 = not defined (doesn't mean anything)

3. 0/0 = indeterminate (may be anything - everything)

4. 0 X 0 = 0

5. 0 X anything = 0

6. 0 + anything = anything

7. 0 + 0 = 0

8. |0 - anything| = anything

9. 0 - 0 = 0

Now, let us try to extend the same operations to infinity:

1. ∞/anything = anything times less than ∞!

2. Anything/∞ = ? (Does it mean anything? - see below)

3. ∞/∞ = indeterminate (may be anything - everything)

4. ∞ X ∞ = ∞ (not super ∞!)

5. ∞ X anything = ∞ (not anything times ∞!)

6. ∞ + anything = (not ∞, but anything) = anything

7. ∞ + ∞ = ∞ (not double ∞!)

8. |∞ - anything| = can no more remain ∞ since it is less than ∞! What then?

9. ∞ - ∞ = 0

Now, let us investigate into another operation:

10. ∞ X 0 = ?

It means infinity added to itself (zero - 1) = -1 times ;or, in other words, ∞ subtracted from itself (∞) 1 time, which comes out to be a clear zero.

It also means zero added to itself infinite numbers of time.

In both the cases, it is bound to be zero.

Therefore,

10. ∞ X 0 = 0

Now, let us investigate into operation 2 with infinity in the light of operation 10:

Anything divided by infinity means number of times infinity would be needed to be subtracted from 'anything' in order for this 'anything' to be left less than infinity.

But this 'anything' is already less than infinity!

Let's do the same thing with finite numbers:

Conceptual Approach:

21/5 conceptually means number of times 5 is to be subtracted from 21 in order to get a number less than 5.

That's why operation 2 with zero was not defined, simply because 0 couldn't be subtracted from 'anything' any number of times in order to get a number less than 'anything'.

How many times can we subtract infinity from 'anything' in order to get a number less than 'anything'?

The only refuge that comes to mind is zero.

But ∞ X 0 = 0!

Therefore, infinity subtracted from 'anything' zero times will simply not be able to get a number less than 'anything'.

Operational Approach:

Or, 21/5 means (operationally - the method!) multiplying 5 by 4 and getting the remainder less than 5!

That's why operation 2 with zero was not defined, simply because 0 couldn't be multiplied with any damn number to get the remainder less than 'anything'.

What about operation 2 with infinity?

Multiply infinity with anything (not 0) and you can't get a remainder since infinity multiplied with anything is infinity and hence, more than 'anything'.

Multiply infinity with zero and the remainder you get is 'anything' itself, which is not less than 'anything'!

It could only have been possible if infinity multiplied by zero were indeterminate (i.e. a finite number) which it is not.

Hence operation 2 with infinity is also not defined, exactly like it is not defined with zero.

Now, let us replace 'infinity' with '0' in operations 1 to 9 with infinity:

1. ∞/anything = anything times less than ∞!

2. Anything/∞ = ? (Does it mean anything? - see below)

3. ∞/∞ = indeterminate (may be anything - everything)

4. ∞ X ∞ = ∞ (not super ∞!)

5. ∞ X anything = ∞ (not anything times ∞!)

6. ∞ + anything = (not ∞, but anything) = anything

7. ∞ + ∞ = ∞ (not double ∞!)

8. |∞ - anything| = can no more remain ∞ since it is less than ∞! What then?

9. ∞ - ∞ = 0

Which, by doing so get reduced to:

1. 0/anything = (anything times less than 0!) = 0

2. Anything/0 = not defined (doesn't mean anything)

3. 0/0 = indeterminate (may be anything - everything)

4. 0 X 0 = 0 (not super 0!)

5. 0 X anything = 0 (not anything times 0!)

6. 0 + anything = not 0, but anything

7. 0 + 0 = 0 (not double 0!)

8. |0 - anything| = (can no more remain 0 since it is less than 0! What then?) = anything

9. 0 - 0 = 0

Now, remove all the bracketed quotes (used for understanding operations with infinity) from the above set, and we are left with:

1. 0/anything = 0

2. Anything/0 = not defined (doesn't mean anything)

3. 0/0 = indeterminate (may be anything - everything)

4. 0 X 0 = 0

5. 0 X anything = 0

6. 0 + anything = anything

7. 0 + 0 = 0

8. |0 - anything| = anything

9. 0 - 0 = 0

And we get the set of operations with zero back, exactly as it was!

It simply proves that, mathematically, zero and infinity are but the two different names given to the same concept as far as number system is concerned.

Or, they are the two sides of the same coin.

Or, they are the two extremities of the same spectrum, which wraps around its own self!

Next week, I'll be going into the physics of zero and infinity.

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