Why is it that x^0 = 1 ?

Frankly, factorials and calculus stuff is far more coherent than this integer , 0.

However, there’s one number that loves to snug into 0, it’s none other than  1. They get going like two peas in a pod , always !

Here’s an occurrence of this cushy approach to 0 & 1.

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You're knotty ! Naughty too !

The main question that I’ve been attempting to fathom from 5th grade : Why  should any number (except zero) raised to the zero power must equal 1?

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Challenge Accepted ?

Variable is something most of us dislike in the field of mathematics…

But it’s not that worse , if we try to imagine it the other way around…

In the mean-time, I came across this stunning problem,

√{x √(x  √[x ……  ])}

It goes on until forever …

By the way , here’s a better way to understand it :

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And you need to find the simple and lucid solution ! ( a bit complex )

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Kaprekar’s 6174

6174 is a very interesting number. Indeed, the number 6174 is also known as the Kaprekar constant, named after the Indian mathematician Dattaraya Ramchandra Kaprekar who studied the mystery behind 6174.

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Dattaraya Ramchandra Kaprekar, Inventor - 6174

So what is all the hoopla about 6174? Well, first, try out arranging the digits such that you have the highest number (7641) and also the lowest number (1467), and then determine the difference between the two, you arrive at 6174 (7641 – 1467 = 6174).

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The Quest Of The Sixy Numbers

The question’s peculiar, the quest is mind twisting,  just one hint provided by me , you need to be an expert at mathematical operation and the knowledge of them.

imageThe Quest is to use 3 and only 3 whole numbers repeatedly between 0 & 9 and to add between the 3 selfsame numbers , any mathematical operation – roots, factorials, division , etc…. to obtain 6 as the result of all collective operations with numbers !
For example : 2+2+2 = 6 , likewise you are required to proceed the same way for the numbers between 0 & 9

The answer seems to be easy,  ummm…. I don’t think so .

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Even – Natural Number Paradox

It is usually ingrained in our minds that the quantity of natural numbers is obviously more than the even numbers because even numbers are just a segment of natural numbers…

But would you believe that there are as many even numbers as natural numbers ?

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Number Pyramid

1 * 9 + 2 = 11
12 * 9 + 3 = 111
123 * 9 + 4 = 1111
1234 * 9 + 5= 11111
12345 * 9 + 6 = 111111
123456 * 9 + 7 = 1111111
1234567 * 9 + 8 = 11111111
12345678 * 9 + 9 = 111111111

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Is 11 Amazing or a mere marvel ?

Interesting ? Furthermore, the subtraction between 12 and 1, 123 and 12, 1234 and 123,…are all correspondents to the answer of the right hand side , here’s how :

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Freezing The Speed Of Light

I’ve been wondering about this concept lately…

When we play a video , say of 10 seconds , we may see objects in motion there. What about 1 seconds, well you’d still see something moving then if it moves fast enough.

100th of a second? The speed of sound ( sound waves particularly, so that they are visible moving )…. You’d proceed decreasing this fraction of the second until thousands and finally when you play that short ( if technology permits ) bit of the fraction, even the speed of sound waves would be seen still !

It then occurred to me, what’s the length of that fraction in which you’d see the Light actually freeze!!!

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