proof that 2 = 1

[haferhole1]

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_Gu3st]

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.

[Bakster]

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

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

[zzboots]

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

[Bakster]

That's what I said

[zzboots]

lol 

*hands zachary the congressional medal of honour* 

I would have settled for a cookie.   

Mmm...cookies.. 

[zzboots]

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.

[Reg50]

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.

[zzboots]

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.

[zzboots]

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. 

[The_Gu3st]

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

[Lowgravity]

wtf

[zzboots]

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. 

[Bakster]

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.

[Dodger]

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