Mathematics

So, how are you people doing with the two problems I gave you? Like it? HAHAHA. Alright, to those who had some hard time with the two questions, hold your breath! There's nothing bout that today. Hee. :p Sorry for those who are waiting for the third part. I am not going to update this series now. Thanks to my tutor who got me into this math thing again. Proving something really interesting. 

I really want to share this with you but not now. He gave us 3 maths problems to prove. However, I only managed to prove 2 of them, which according to him, that's SUPER EASY and Slightly easy. I am yet to prove the SIPEH (super, incredibly, riddiculusly _____(insert whatever you like) HARD proof. I already spent my whole afternoon trying to prove it. However, still I failed. Damn! 

Some of you might be wondering why I am so obsesed with it? After all, it's just a math problem. Honestly, this is not about math now. I admit I am really facinated by numbers and math, however, sometimes pride is the issue also. He told us a story behind this proof. I will tell you the whole story after I figure out the proof. I will only tell you how lame you are if you are unable to proof the question that I am going to post later in this post. This math problem is being proved decades ago by a BOY! He's only 7 year old then. Now? Harlo! How old are you now? If you can't prove this, you lost to a kid man. LOSER! (Well, that's what kept me cracking my head for this afternoon.) However, I solved it in the end. It's this another problem that makes me go cockoo whole afternoon! 

Nevermind bout that, just to make some noise bout losing to a kid. Hee. So here are the questions. I will post the answer some other time.

Let S = { 1, 2, 3, ... , 100}

n(A) = 51

A is a subset of S

I know some of you are thinking what the hell is this?

let me explain. S is a set which contains all the numbers from 1 to 100.

now 51 numbers were chosen randomly. 

Alright?

Now prove that 

i) There exist 2 numbers in the 51 chosen numbers such that the sum of these 2 numbers is 101.

ii) There exist 2 numbers in the 51 chosen numbers such that the Highest Common Factor (Greatest Common Divisor) of these 2 numbers is 1. 

*this is what the KID proved*

iii) There exist 2 numbers in the 51 chosen numbers such that one of the number can divide the other number completely. 

*this is where I got stuck*

So enjoy proving this. Muahahahaha.

for now, I will continue to crack my head.

- =.= -

Wonders of Numbers - Part II

Welcome back to another part of Wonders of Numbers. Today, we will be discussing about inequality. Don't know what inequality means? It means not equal (literary). So, has anyone got any idea of what I am going to say? Drum please... Applause... AAAAAAAAAAAAND THIS IS THE TOPIC! INEQUALITY! 

(I know it's a lame joke, sorry for that)

Alright. Let's get to the main topic now. I am not going to teach you what inequality is cause what I am going to share now is very basic for those who had taken Add Math and I will make it as simple as possible for those who doesn't know what Maths is all about. But first of all, you have to recognise some symbols.

1. equal to -- =

2. greater than -- >

3. less than -- <

4. greater or equal to -- >= 

5. less or equal to -- <=

6. not equal to -- !=

* I got these symbols from C++, it's faster for me to write in this form

So let's start of with some simple Mathematics. 

1. Learn some number classification.

Integers and Rational numbers.

Integers are whole numbers, positive and negative numbers. NO FRACTIONS NO DECIMAL POINTS!

Rational numbers are fractions of 2 integers. where the denominator is not 0. eg. 1/2, -3/9.

Alright we can start now. Most of us know that fractions are also numbers and decimal are also numbers. So they are actually equal at some point. Say 1/2 = 0.5 and 7/8 = 0.875. All fractions can be changed into decimal form but not all decimal can change into fraction form. I'll give you an example of a decimal number which can't change into fraction form or we say rational numbers. Try changing 1.414213562 into a fraction (rational number). How do we know that this number can be changed into fractions? So there is a basic rule. If your decimal number has some numbers been repeating at the back. it can be changed into fractions.

eg. 0.111111111111... = 1/9 

you can see that 1 is repeating

eg. 0.923076923076923076... = 12/13

notice that 923076 is repeating

So we made a conclusion that all number with some numbers being repeated at the back can be changed into fraction. For those in Form 4 and Form 5, remember changing some stupid numbers into fraction form using the Geomatric Series Rule and the Sum To Infinity of a Geometric Series? S = a/(1-r)? Alright now try changing 0.9999999....9999...99...9999 into a fraction. Now first thing first, answer this question.

Is 

A) 0.9999999999999...9999999...999999....99999 = 1 ? Or you say that 

B) 0.99999999999...99999999...9999999...9999 <>

Don't bluff! I know u chose A. Yeah everyone will choose A base on what they see. 

Now let us work this out and you will not believe what you see! Math is Magic!

So we use the geomatric way i mentioned just now.

So 0.99999999999....999999...99999...9999... = 0.9 + 0.09 + 0.009 +... right?

There for we have a Geometric Series of 

a = 0.9 and r = 0.09/0.9 = 0.009/0.09 = 0.1 or 1/10.

Use the formula of Sum To Infinity. ( This series has no end cause its a convergent series, the limit will goes to 0 (zero) when the number of terms goes to 00 (infinity).

So the formula is S = a/(1-r) --- if you don't believe me, google it.

So S = 0.99999999999999....9999999999...9999999... right?

S = a/(1-r)

S = 0.9/(1-0.1)

There for we put 0.9999999999999.....99999999......999999.... back into the S

0.99999......9999999.....9999999... = 0.9/(1-0.1) = 0.9/0.9 = 9/9 =1

So we make a conclusion that, 

0.99999999...9999999...99999 = 1

Now do u agree? NO? DON'T LIKE IT THIS WAY? Ok, I'll show you and esier way. 

0.9999999.....999999999...99999..99999 = 0.6666666666666...66666... + 0.33333333333...3333333...33333 right?

and 0.6666666666666666666....6666666666....666666... = 2/3

and 0.3333333333333333333...33333..333333...3333..... = 1/3

so 0.999999999........9999999.......999999.... = 2/3 + 1/3

      = 3/3

      = 1

Now you agree? Just accept it. Now Math has once again shown its Magic to you.

Challenge my theory.

Wonders of Numbers - Part I

Harlo! After so long, let you know more about myself if you haven't. 

1. My mom is a Form 6 Math teacher.

2. I got offered a place in UKM for Math but I chose to be in UTAR for Actuarial Science.

3. I never get anything less than B for Math.

4. I enjoy the thrill when I managed to solve a math problem.

So I think by now you are thinking why this guy is all about Math? Yeah I like numbers, not Numb3rs. I am fascinated by all the numbers and their theory and sometimes the working that you just can't prove it with the Math theory. You know, the magic of Math! You will go WOW! OOO! WHOA! *CLAPS* when you see something interesting about Math. I'll show you some MAGIC for the posts to come.

This Magic, I learnt it when I was attending a camp 2 years ago. (It involves some knowledge of alphabets and countries also.)

So you just follow the steps k?

1.  Think of a number between 1 - 9.

2. Multiply the number by 9.

3. You will get a 2-digit number. Add both the number and result it to 1-digit number. (eg. 88 -> 8+8 = 16 -> 1+6 = 7)

4. Subtract the 1-digit number you get by 5.

5. So let's change the number you just got to alphabets. 

1 --> A

2 --> B

3 --> C

4 --> D

5 --> E

6  --> F

7 --> G

8 --> H

9 --> I

6. So you get your alphabet already?

7. Now, think of a country starting with that alphabet.

8. Got it? Ok, now go back to the alphabet you got just now. You will think of an animal starting with the alphabet after your alphabet. (eg. if you get K, the next alphabet is L)

9. OK? So now, put the animal into the country you are thinking. (eg. ELEPHANT in DENMARK - 99% of you matches my example.)

10. Applaud please.

Hehehe. How do I know? Ok, unless you are really familiar with countries with D and animal other than E, you will be thinking Elephant in Denmark. There's an alternative to the country though. Dominican Republic. As for the animal, I am yet to discover something with E. If you have any idea, post it in the comments. 

So you want to know the magic? Yeah I bet you want to. Now you have to promise me 1 thing. Take this unbreakable vow!

I, (your name), solemnly swear to spread this piece of great shit around and trick my friends into loving MATH!

*This is not a chain mail. Nothing bad will happen to you if you don't forward it withing 99seconds. You will not get kisses from the person you admire secretly if you forward this within 3 seconds.

Alright! Secrets reveal. 

It is a known fact to many mathematician, especially those who are good in mental arithmetic. The trick starts when I ask you to multiply your number with 9. It is proven that if you multiply a number with 9, the sum of all the digits from your product will eventually become 9 when u add it until it become a 1-digit number.

eg1. 8960986 x 9 = 801548874

8+0+1+5+4+8+8+7+4 = 45

4+5 = 9

eg2. 7649512 x 9 = 68845608

6+8+8+4+5+6+0+8 = 45

4+5 = 9

eg3. 56772851 x 9 =510955659

5+1+0+9+5+5+6+5+9 = 45

4+5 = 9

By these 3 example, you can see that I randomly pick any number and multiply it by 9. When I sum all the digits in the product up, I will get a 9 in the end. With this, I am already MANIPULATING your mind. I make you subtract 5 from 9, which will result in 4. You will get D. with limited countries starting with the alphabet D, you will choose a better known country - Denmark. I make you think of an animal starting with the alphabet next to D, which is E, you will think of the easiest and largest animal on land - ELEPHANT.

That's how I know what you are thinking. Elephant in Denmark. MUAHAHAHAHA.

Isn't numbers just fun? Math is even better. Like my mom always says :

"Math is like a piece of music, the numbers are the notes on the grid, the way you put the numbers together and solve a problem is like putting all the notes together and play the music. When you hit the right note, you produce a piece of beautiful music."

As well as what my Professor says:

"Math is an ART. It is for those who really see the value in it to see the beauty in it. I don't know what Picasso or Leonardo da Vinci is drawing so I don't see the beauty in it. I don't think most of you know what Math is really all about, so you don't see the beauty in it."

Math, unknowns and numbers always come together. Enjoy numbers and you will enjoy math. Again, I want to stress that numbers is not the series NUMB3RS. This is totally different from what I am telling you now.

 

坚持

头前的路

thao cheng eh lor

(The road in front)

不知多长多呢苦

mm zai ua deng ua nee khor

(don't know how far and torturing)

看不著

khua boay tiok

(Can't see)

走著一步算一步

kia tiok ci bor s'ng ci bor

(a step will be a step)

雨水那落

hor zui na lok

(If the rain falls)

已经渥湿阮衫裤

yi king ark tam gun sa khor

(it will make my shirt and pants wet)

这阵风

ci zun hong

(This wind)

之是乎阮的心更加坚强

ci si hor gun eh sim kin kar kien kiong

(is only to make myself stronger)

成功的背后

seng kong eh poay ao

(Behind every success)

无知有多少苦楚

mm zai wu ua zhe khor chor

(don't know how much effort there is)

阮选择的路

gun xuan tit eh lor

(The road I chose)

一定坚持到成功

yi ding kien qi gao seng kong

(I will hold till I succeed)

坚持的心伴阮向前走

kien qi eh sim pua gun hiong cien kia

(Determination will walk with me) 

请你会记得阮的名

cia li eh ki tiok gun eh mia

(please remember my name)

有人出世就好命

wu lang chu si jiu ho mia

(Some people is borned lucky)

阮是用命在打拼

gun si yong mia tit pha pia

(I fight with my life)

勿怕失败慢慢向前走

mm kia sit bai ban ban hiong cien kia

(Don't be afraid of failure and slowly walk) 

运命不是天注定

wun mia mm si ti zu tia

(fate is not determined by god)

只要用心来打拼

ci yao yong sim lai pha pia

(As long as we work hard)

一定唱出阮的名

yi ting ciu chu gun eh mia

(we will make our name big)

This whole song is actually about being strong and keep holding onto our choices in life. When we made our choice, we will hold onto it. If we have the determination, we will be successful one day. By the way, it's a hokkien song. Hee.