Stupid Math problem, looking for explanation!

[Snoop]

Just wondering what the explanation was for this:
a = b
a² = b²
a² - b² = ab - b²
(a + b) (a - b) = b(a - b)
divide (a - b)
a + b = b
?????

 

[joemamma]

i swear this has been done before on anadtech...anyways, dividing by (a-b) means you're dividing by zero....

 

[Snoop]

srry joemamma, I just saw it today, ill do a search 😀

 

[Alphazero]

Originally posted by: Snoop
Just wondering what the explanation was for this:
a = b
...
divide (a - b)

Division by zero.

 

[Snoop]

10-4

 

[UglyCasanova]

~~~You must take the way of the locust, search your heart, and all will be revealed.~~~

 

[rgwalt]

Also, I'm not seeing where the third step comes from...

Ryan

 

[Viper GTS]

Originally posted by: rgwalt
Also, I'm not seeing where the third step comes from...

Ryan

Substitution, if a=b than b²=a*b.

Viper GTS

 

[rgwalt]

Originally posted by: Viper GTS

Originally posted by: rgwalt
Also, I'm not seeing where the third step comes from...

Ryan

Substitution, if a=b than b²=a*b.

Viper GTS

Ah, thanks. I'm used to having my hand held a little more when working through these kinds of proofs.

Ryan

 

[silverpig]

Hmm, I wonder if this suggests that 0/0 is an actual number.... The entire thing is true if a = b = 0.

 

[Noriaki]

Originally posted by: rgwalt
Also, I'm not seeing where the third step comes from...

Ryan

That's okay, that's the step where the whole thing starts falling apart.

You use a=b, then substitue a*b for b², then you subtract b² from both sides.

To perform that step you have to assume a=b. Which is okay...but it bites you in the butt later in this "proof".


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

Since a=b has to be true, for the 3rd step to be true this step is actually:
(a+b)(0) = b(0)

Which is also okay because 0 = 0.

But you can have any quanity x and any quantity y and say 0x = 0y.
That doesn't mean x = y.

And you can't divide both sides of 0x = 0y by 0 and conclude that x = y. The 0s don't cancel like that. That's not how division by 0 in standard "newtonian" mathematics works.

 

[Noriaki]

Originally posted by: silverpig
Hmm, I wonder if this suggests that 0/0 is an actual number.... The entire thing is true if a = b = 0.

Yeah but then a+b = b just says that 0+0 = 0.

Which is first principles of addition, you don't need to fool around with limits to do that.

 

[joemamma]

Originally posted by: Snoop
srry joemamma, I just saw it today, ill do a search 😀

no need to apologize,,,i was just saying it had been done before on anandtech but not recently...hope we helped

 

[silverpig]

I know. That's exactly my point. Because 0 + 0 = 0, then that set of statements is true, including the 0/0 = 0/0...