Wonder Numbers: 0 , 1, ∞ and To Understand Division by grouping mechanisms

Wonder Numbers: 0 ,  1,  ∞

1.       NOTHING IS SOMETHING ?

Nothing is symbolized by 0.

Something is symbolized by 1 – the least value number.

i.e.  0 = 1 ?

Steps to prove the above statement:

1 + ∞  =  ∞  (Assumed) – on the assumption - even if you add any number to infinity, the resultant number will be infinity only. )

Then, 1 =  ∞ - ∞ = 0 ! 

Something is Nothing and Nothing is Something.

See the calculation below:

In 1 +  ∞  = ∞ + x , because some value is being added to infinity.

i.e. 1= ∞ + x – ∞ = ( ∞ - ∞ ) + x = 0 + x = x

Then 1 = x.

That proves that if we add a number to infinity, infinity also changes its value.

Hence 1 + ∞ = ∞ proves to be wrong, but, it should be ∞ plus.

Even the least value number say 1, adds value to the very large number i.e. infinity?

2.       Multiplication:

1.       Something multiplied by nothing becomes Nothing.

2.       Even infinity multiplied by nothing becomes Nothing.

Nothing becomes powerful compared to addition.

Example for item 1 above: 1 x 0 = 0

Example for item 2 above: ∞ x  0 = 0

3.       Division:

Nothing divided by something becomes Nothing.

Nothing divided by infinity also becomes Nothing.

But,

Something divided by Infinity becomes Infinity! – Perhaps valid argument to show the benefit of sharing by division.

Infinity divided by nothing becomes infinity.

O /  1  =  0     &     0 / ∞  =  0.

But,

1 / ∞ = ∞    &    ∞ / 0 = ∞.

Fallacy or wonder of maths:

To prove:

0 / 0  = 1 ?

Steps:

0 / 0 = 1  - assuming 0 as any other number like 1,2,3 et.  i.e. 3/3 = 1 and not 3. Hence 0/0 can be reasonably assumed to be 1 and not 0 on the above analogy. 

Take the equation:   0 / 0  =  1

i.e. 0 = 1 x 0 = 0

Hence, 0 / 0 = 1 is correct.

Let us apply the same principle to multiplication:

0 x 0 = 0

Divide by 0 the above equation.

0 x 0 / 0 = 0 / 0.

Applying our findings of 0/0 equals 1, the above will be: 0 x 1 = 1 i.e. 0 = 1 / 1.

i.e. 0 = 1?

To Understand Division by grouping  mechanisms

6 divided by 2 =  3.

Method:

 In the above there are two rows of 6 blocks. Because we have to divide 6 by 2.

Now, group these 12 blocks into 2 blocks each. Then again group them clubbing 2 together.

 

1 & 2 – group A

  

3 & 4 - group  B

5 & 6 – group C  

7 & 8 – group  D

9 & 10 – group  E

11 & 12 – group F

Note: A & B one Group; C & D - another group; E & F - third group

You are having three groups and the answer is 3.

Now, 7 divided by 2 = 3.5

How to get it.

 Group the above block into blocks of two as above.

1 & 2 – Group A

3 & 4 – Group B

  


 

5 & 6 - Group C 

7 & 8 – Group D

9 & 10 - Group E 

11 & 12 – Group F

13 & 14 – Group G  - There is no matching block and is remainder block.

Then group them into two and again group into 2.

We have 3 fully matching blocks and one remainder block.

Hence answer is: 3.remainder block.

Now we have to find the value of remainder block. 

4 blocks mean one number and here we have 2 blocks – 13 and 14. Ie. Half. i.e. 0.5.

Hence the answer is: 3.5.

A Tale of Two Seas

A Tale of Two Seas

Sitting in the Geography class in school, I remember how fascinated I was when we were being taught all about the Dead Sea. As you probably recall, the Dead Sea is really a Lake, not a sea (and as my Geography teacher pointed out, if you understood that, it would guarantee 4 marks in the term paper!) 

It is so high in salt content that the human body can float easily. You can almost lie down and read a book! 

The salt in the Dead Sea is as high as 35% – almost 10 times the normal ocean water. And all that saltiness has meant that there is no life at all in the Dead Sea. No fish. No vegetation. No sea animals. Nothing lives in the Dead sea. And hence the name: Dead Sea. 

While the Dead Sea has remained etched in my memory, I don’t seem to recall learning about the Sea of Galilee in my school Geography lesson. So when I heard about the Sea of Galilee and the Dead Sea and the tale of the two seas – I was intrigued. Turns out that the Sea of Galilee is just north of the Dead Sea. Both the Sea of Galilee and the Dead Sea receive their water from river Jordan. And yet, they are very, very different. 

Unlike the Dead Sea, the Sea of Galilee is pretty, resplendent with rich, colorful marine life. There are lots of plants. And lots of fish too. In fact, the Sea of Galilee is home to over twenty different types of fishes. 

Same region, same source of water, and yet while one sea is full of life, the other is dead. How come? 

Here apparently is why. The River Jordan flows into the Sea of Galilee and then flows out. The water simply passes through the Sea of Galilee in and then out – and that keeps the Sea healthy and vibrant, teeming with marine life. 

But the Dead Sea is so far below the mean sea level, that it has no outlet. The water flows in from the river Jordan, but does not flow out. There are no outlet streams. It is estimated that over a million tons of water evaporate from the Dead Sea every day. Leaving it salty. Too full of minerals. And unfit for any marine life.

The Dead Sea takes water from the River Jordan, and holds it. It does not give. Result? No life at all. 

Think about it. 

Life is not just about getting. It’s about giving. We all need to be a bit like the Sea of Galilee.

We are fortunate to get wealth, knowledge, love and respect. But if we don’t learn to give, we could all end up like the Dead Sea. The love and the respect, the wealth and the knowledge could all evaporate. Like the water in the Dead Sea.

If we get the Dead Sea mentality of merely taking in more water, more money, more everything the results can be disastrous. Good idea to make sure that in the sea of your own life, you have outlets. Many outlets. For love and wealth – and everything else that you get in your life. Make sure you don’t just get, you give too. Open the taps.

And you’ll open the floodgates to happiness.

Rhythm helps children master math problems

An innovative use of rhythm in a music- based programme enabled school kids score significantly higher on math tests than peers who received regular instruction.

“Academic Music” is a hands-on curriculum that uses music notation, clapping, drumming and chanting to introduce third-grade students to fractions. Co-designed by San Francisco State University researchers, it addresses one of the most difficult and important topics in the elementary math curriculum.

A fraction represents a part of a whole or, more generally, any number of equal parts. A fraction describes how many parts of a certain size there are, for example, one-half, five eighths, three-quarters. “If students don’t understand fractions early on, they often struggle with algebra and mathematical reasoning later in their schooling,” said Susan Courey, assistant professor of special education at San Francisco, the journal Educational Studies in Mathematics reported.

“We have designed a method that uses gestures and symbols to help children understand parts of a whole and learn the academic language of math,” added Courey, according to a university statement.

“Lower-performing students might find it hard to grasp the idea of fractions from a diagram or textbook, but when you add music and multiple ways of learning, fractions become second nature to them,” added Courey.

Courtesy: The Deccan Herald. 

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04-03-2012