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ill go 1 step at a time

Assume that

a = b

Multiplying both sides by a,

a² = ab

Subtracting b² from both sides,

a² - b² = ab - b²

Factorizing both sides,

(a + b)(a - b) = b(a - b)

Dividing both sides by (a - b),

a + b = b

If now we take a = b = 1, we conclude that 2 = 1



math is power!

The math is interesting, but if a=b=1 then why dont they both just be "a" or both just be "b"? The manipulation of the equation you performed is right, but the technical math is flawed. Im pretty sure that one of the rules of algebra state that in any one given equation, no two variables will equal the same thing. If you try doing that same math from the very beginning by inserting 1 for both of those variables, you get a true, logical statement.

If I got a penny every time I saw this...

I won't spoil it for anyone, but I'll PM haferhole

Quote from: The_Gu3st on November 14, 2005, 11:19:10 PM
The math is interesting, but if a=b=1 then why dont they both just be "a" or both just be "b"? The manipulation of the equation you performed is right, but the technical math is flawed. Im pretty sure that one of the rules of algebra state that in any one given equation, no two variables will equal the same thing. If you try doing that same math from the very beginning by inserting 1 for both of those variables, you get a true, logical statement.

pffft.   ::)


The reason this works out is because a - b = 0
And when you divide by zero funny things happen, this case the resultant is an illogical statement.  :-\

You finished the proof wrong however though.

at a + b = b  you substitute b in for a

so 2b = b  and divide by b

leaving us with 2 = 1

You can't arbitrarily set variables equal to a number half way through the proof ;)

That's what I said :P

Quote from: virtuoso on November 16, 2005, 01:08:33 AM
lol  :D

*hands zachary the congressional medal of honour*  ;)

I would have settled for a cookie.   :-[

Mmm...cookies..  :D

Quote from: virtuoso on November 16, 2005, 01:41:53 AM
No cookies for you chubby : D

Hey, I just started working out again.

But I assure you that I have never lost my girlish figure.

First off you can't multiply by (a) anyway because it's an only varible and Therefore multiplying it by itself can't be done because there is only one (a) not two.

Quote from: Reg50 on November 20, 2005, 01:00:33 AM
First off you can't multiply by (a) anyway because it's an only varible and Therefore multiplying it by itself can't be done because there is only one (a) not two.

lol...  ::)

This is very untrue at best.

You can multiply through by a varible as long as equality is preserved aka right side equals left side.

say 5x = 2y  within the laws of math, you can multiply both sides by lets say 4 so it would become 20x = 8y

instead of a number, lets use a variable, joy. and lets use x, more joy.
5x^2 = 2xy is the same thing as 5x = 2y
They are just being expressed differently.

I hope that cleared things up.

Since we are on the subject of weird math, I thought it would be fun to include a bit more for your enjoyment.  I tried to explain this concept to my dear friend blitzy, but he disbelieved me and ran away.  :'(

So on with the math...

This involves repeating decimals.  Everyone knows that .333repeating = 1/3.  But did you know that .999 repeating = 1?  Let me show you how. ;)

First let me show how you convert a repeating decimal into a fraction.

Say x = .333 repeating    if you multiply both sides by 10 you get

10x = 3.333 repeating  Now you subtract the first equation from the second

  10x = 3.333 repeating
-x = 0.333 repeating
   9x  = 3
   x= 3/9  = 1/3

Now apply same method to .999 repeating

x = .999 repeating     multiply both sides by 10
10x = 9.999 repeating   and again we subtract 1 from 2

  10x = 9.999 repeating
-x = 0.999 repeating
   9x  = 9
   x= 9/9  = 1/1


And there you have it.  Just another fun math trick.  Feel free to show off  your amazing new math skills at school.  Then quickly get beaten up for it. ;)

To Blitz: Pwned.  :D

Is it true though? Or is it just a "math trick" as you said. There isnt any known flaw of why that happens?

wtf ???

Quote from: The_Gu3st on November 22, 2005, 11:39:40 PM
Is it true though? Or is it just a "math trick" as you said. There isnt any known flaw of why that happens?

Well .999 approaches 1, but it never actually converges to it.

It's not so much a math trick as a flaw in our math system.  8)

I guess it is a sort of flaw.

But 0.9 R (Recurring) is equal to one.

If you know about boundaries, then 100 to the nearest unit has a lower bound of 99.5 and an upper bound of 105.5, NOT 104.9R. Not only does that look scruffy, but 0.9R equals 1 so we write it as 105.5.

Yes. Lets have a discussion about time-travel instead. It's way more interesting! Eh paulo?  ;)

Quote from: zzboots on November 22, 2005, 11:36:43 PM
Since we are on the subject of weird math, I thought it would be fun to include a bit more for your enjoyment.  I tried to explain this concept to my dear friend blitzy, but he disbelieved me and ran away.  :'(

So on with the math...

This involves repeating decimals.  Everyone knows that .333repeating = 1/3.  But did you know that .999 repeating = 1?  Let me show you how. ;)

First let me show how you convert a repeating decimal into a fraction.

Say x = .333 repeating    if you multiply both sides by 10 you get

10x = 3.333 repeating  Now you subtract the first equation from the second

  10x = 3.333 repeating
-x = 0.333 repeating
   9x  = 3
   x= 3/9  = 1/3

Now apply same method to .999 repeating

x = .999 repeating     multiply both sides by 10
10x = 9.999 repeating   and again we subtract 1 from 2

  10x = 9.999 repeating
-x = 0.999 repeating
   9x  = 9
   x= 9/9  = 1/1


And there you have it.  Just another fun math trick.  Feel free to show off  your amazing new math skills at school.  Then quickly get beaten up for it. ;)

To Blitz: Pwned. :D

thats no trick!

.999 is just three times larger than .333 so when you put the two numbers into the same formula it makes sense that the outcome would be 3 times larger!!! The only reason it seems weird is because he used decimals to display it, if you use whole numbers its really basic!

It's obvious that .333 is a third, and tripling a third makes one. Tripling .333 makes .999, so .999 = 1.

It's obvious that 1/3 can not be properly expressed as a decimal and .333 is a rounded number that never ends......It does not equal one. Two different numbers equaling each other does not happen.

http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=print;num=1027804564

for anyone who doesnt believe me, read Kozo's posts.

I will very simply use zz's  little proof to prove you wrong.

Quote
  (he set x as .999...)
  10x = 9.999 repeating
-x = 0.999 repeating
   9x  = 9
   x= 9/9  = 1/1

note: zz tried to argue that when he subtracted from 10x=9.999... he was not subtacting x from both sides, but x=.999... from the whole equation. He set x=.999... at the beginning of the equation, so x stands for (.999...), which is what you are subtracting by taking x from both sides. So for easier understanding I will subtract x from both sides.

we will use (...) to represent repeating decimals, in which the number directly before the (...) is the repeated one.

so

x=.999...98
*multiply both sides by ten*
10x=9.999...98
*subtact x from both sides(note x=.999...98)*
9x=9
x=1

so .999...98=.999...=1

for sake of time it can be know that by using that equation would say that

.999...91(through).999...89=1 well it seem a lot of different numbers are equal to one?

Basically stating, somthing is flawed with the equation. It would set masses of numbers equal to each other.......which is not true.

I have read things that state you can't mutiply a repeating number by a value with a 0 in it, but these seem to use basic arithmetic proof example. It says that you will continue to multiply by zero (since the 9s are infinite)

example
17
x10
    00
+170
170

.999...
x10
000000000(infinite)

not too sure of that, but you can't divide by zero(using the same type of principle) either, so it may have some substance.

Basically the proof is flawed, and I'm not sure of the correct way to represent this(though I know there is a way)

n=number of repeating decimals

.999n = 1 - .000n1

Sigh, Blitz is speaking of topics way above his head.  :'(

I merely learned my examples while in math class...

But let me so kindly point out where he went wrong.

A: Blitz doesn't know the difference between subtracting x and subtracting an equation.  If he wants to subtract x, he can, but he would have to substitute back in for x, frivolously taking more steps.

B: x = .999....98 is not a repeating decimal

look what happens when we keep things simple.  And add some random 8 on the end of a repeating decimal...  ???


say we start with  x = .99998
multiply by 10
10x = 9.9998  and since blitz likes to be difficult. we will subtract x from both sides
9x = 9.9998 - x  and now we can substitute .99998 back in for x.
9x 9.9998 - .99998
9x = 8.99982
x = 8.99982/9   


WHAT?!? HUH? exactly...see..

        9.9998
      -  .99998
        8.99982

a repeating decimal repeats.  Blitz's example does not.

C: For the rest of his argument...It is just a bunch of fancy stuff he does not understand.  Just because it is on the internet it doesn't make it true.  ;)

I would gladly discuss anything you thoroughly understand, but I am not going to waste time on random stuff said by others.

Sadly, Blitz said he will be leaving the duelboard community.  Apparently we are all "too immature".  Hopefully one day, after a decent math class, he will come to realize his errors.

A moment of silence for dear blitzy...  :'(  :'(  :'(  :'(  :'(  :'(

*edit* mispelled silence.

*edit* The tears continue... 
:'(  :'(  :'(  :'(  :'(  :'(  :'(  He is going to block me from aim :'(  :'(  :'(  :'(  :'(  :'(  :'(

Quote from: zzboots on December 03, 2005, 01:01:56 AM
Sadly, Blitz said he will be leaving the duelboard community.  Apparently we are all "too immature".  Hopefully one day, after a decent math class, he will come to realize his errors.

A moment of silence for dear blitzy...  :'(  :'(  :'(  :'(  :'(  :'(

*edit* mispelled silence.

*edit* The tears continue... 
:'(  :'(  :'(  :'(  :'(  :'(  :'(  He is going to block me from aim :'(  :'(  :'(  :'(  :'(  :'(  :'(

Wow, you guys got into a fight over a math problem? Come on you guys, if anything, thats immature in itself...wow.

Did something precede this event? Or did you just go crazy over math?

Quote from: The_Gu3st on December 03, 2005, 03:41:08 AM
Wow, you guys got into a fight over a math problem? Come on you guys, if anything, thats immature in itself...wow.

Did something precede this event? Or did you just go crazy over math?

It's more than the math problem...  :'(

u guys, just let it go, u figured out the 2=1 thing, and thats all that matters, ur getting obbsessed with this ¹/3 thing

Im no math whiz and i think i actually lost weight for how long i pondered this but you guys gradually changed the original trick the original trick used .999 REPEATING which by my calcumulations (spelled wrong on purpose)doesnt work. However it does seem to be a trick when the number is not repeating(.9998) who knows. maybe my brain is fried, i have been away from the classroom for a year...its quite possible!

i hate math

(http://allproducts.com/manufacture97/abidfish/product1-s.jpg)

Maths is great.