How is my 2 = 1 equation wrong?

[sash1]

damn, everyone does derivitives differently. Well, I'm in AP Calculus, so I'm saying my way is right.

lim (/\x -> 0) f(x+/\x) - f(x) / /\x

now obviosuly you can't do this, because there is devision by zero as /\ (delta) x approaches zero. I still don't understand what this problem has to do with derivitives though. But you're math is extremely faulty. You have division by zero. And if a-b really doesn't equal zero, then you can't multiply both sides by a (step 3) and subtract b^2 (step 4). These things can only be performed on equations of EQUALITY. So you must substitute your 0 (original equation) by some unknown variable, then go from there.

`K

 

[PrinceXizor]

Originally posted by: Kauru
damn, everyone does derivitives differently. Well, I'm in AP Calculus, so I'm saying my way is right.

No offense meant by this as your explanation is correct, but a high school math class isn't really a solid basis for speaking from a position of strength.

However, I'm being nit-picky. Your explanation is correct (and is a good summation of all the other valid posts). As another poster mentioned, a limit is a value, not an equation. The great benefit of limits is that we can legally mathematically calculate a value (i.e. the limit) where the evaluation of the function might be undefined (for example, because of divide by zero errors). Using limits (carefully and properly) can help us develop other useful ideas in the area of mathematics.

This type of discussion is exactly why improper proofs can be an effective means of teaching and solidifying basic mathematical concepts. A very interesting thread.

P-X

 

[Peter]

Thanks uart for bringing the correct math onto the case. ShawnD1, that's how this "almost equal" thing is supposed to be handled properly, and how the rules of equation solving stay applicable.

 

[martind1]

hey i can prove

4 = 13


now follow this

(a-b) * (b-a^2) = (a^4 - 5) / (b^2*(a+1))


but you have to assume a= 4 or 6 when applicable and b = 29*pi^2 or 3


anything wrong with my math?

 

[Peter]

What math? Random stuff with an equal sign inbetween is not math. Solve that equation to the outcome of 4=13, try to do it mathematically correct, then we'll show you where your blatant mistake is.

 

[martind1]

Originally posted by: Peter
What math? Random stuff with an equal sign inbetween is not math. Solve that equation to the outcome of 4=13, try to do it mathematically correct, then we'll show you where your blatant mistake is.

no, i think you missed a divsion in there, better try it again buddy.

 

martind, I agree with peter, why do you think you are allowed to write a jumble of algebra and stick an equal sign in the middle? Maybe its just that I'm too lazy to do out the math, but those two expressions dont look equal to me at all! Just because there is a number A and a number B that work, the two expressions are not equal. Take X=2X for example, it works for X=0 but quite obvoiusly X!=2X

 

[UCSDHappyAsian]

i did not spend too much time into it.. if i am wrong.. then sorrie wasted your time


every step was right~~
however, in the beginning... it pretty much says a=b=0
in that case... 2b=b, yeilds 0=0
instead of 2=1

 

[UCSDHappyAsian]

mah bad... it did not say a = b= 0
i just asked my landlord was happened to be a math and bioengineering majored..
he said they spend time on this thing couple times in the college..
they also prove the following


A * B is not equal to B * A
by using imaginary number.... not i^2 = -1
not that one...
just an imaginary number

 

[UCSDHappyAsian]

hehe math is crazy...... crazy ppl often come up with crazy formula~~~
dang it
combination of physics and math is even more crazy~~~
i loved the 10 dimentional proof...
if i have time.. i will go buy that book and take a look at it
landlord told me its something about shooting a particle through a hole and somehow it dissappear...
haha.. it was too deep and i did not follow a word of what he said...
anyways.... maybe during the summer i will go buy it


but a taiwanese scholar's recently discovery.....
it proof the ELEMENTS OF PARTICLE to be incorrect....therefore, a lot proofs based of that should be re-considered.........
anyways.. it is crazy

 

[UCSDHappyAsian]

yah.. i was right..
hehe
step 1, 2 , 8 says b is equal to 0

and if u want to draw a conclusion of something..
every step must be consistent.... it means... not just a single step... but each step to another step....

 

[uart]

A * B is not equal to B * A

Well if "*" is regular multiplication and A and B are real or complex numbers then that is simply not true.

Only if you choose some other fields for A and B and some other meaning for "*" then you can have A * B is not equal to B * A. Some examples would be "matrix multiplication, vector cross product and inner products with complex arguments.


Why is it that these maths related threads just seem to get more silly the longer they go on

 

[Cogman]

, just to add in. The = sign means equal to, if you said that a-b -> 0 then a != b. close but not there. everyone else is correct when they say that a-b=0 and therefor x/(a-b) is undefined. I like doing dirivitives the easy way (for single variable dirivitives, non of that dh/dx stuff ) dy/dx=nx^n-1 but nooooo, they had to go and add y's into it. (sorry tired right now so I'm ranting .) BTW. Just as a side note, Our calculus teacher never really explained why the dirivitive of sin(x) = cos(x) and the dirivitive of cos(x) = - sin(x).

 

[imgod2u]

a - b = 0
a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a + b) * (a - b) = b * (a - b)
a + b = b
b + b = b
2b = b
2 = 1

The problem is, you're redefining "=". The laws of mathematics and logic in general relies on a solid definition of "=" to mean equal to. If you redefine it, you will have to re-prove all the other mathematical axioms according to the new definition. E.g. you must prove that a * b = b * c implies a = c. This is true when "=" means equal to, but not neccessarily true when "=" means "close to".

Let's not redefine symbols but instead, explicitly state what you're saying in terms we already have in mathematics (and therefore, have established rules for).

limit as a -> b (a) = b
Your next step was to multiply both sides by [limit as a -> b (a)]. However, none of the limit laws allows this as I recall. The logical mathematical = and equivalence only holds for discrete values.

 

lim(h->0) (cos(x+h)-cos(x))/h = (cosxcosh-sinxsinh-cosx)/h = ((cosh-1)(cosx)-sinxsinh)/h cos0-1=0 sinx for x close to 0 = x (so 0-hsinx)/h = -sinx


for you cogman

 

[t3h1337guy]

After closely examining this whole topic...I have derived that we have way too much time on our hands.

 

[martind1]

Originally posted by: martind1
hey i can prove

4 = 13


now follow this

(a-b) * (b-a^2) = (a^4 - 5) / (b^2*(a+1))


but you have to assume a= 4 or 6 when applicable and b = 29*pi^2 or 3


anything wrong with my math?

still holds true

 

[MrDudeMan]

these threads are so annoying

before i say this, i have taken calculus


these kinds of things incorporate all the stupidity in the people who think they are coming up with something brilliant. you said in your "proof" (proof of you wasting our time to be exact) that a-b=0, and then you say a+b=b. how is that possible? if a+b=b, and then you say b+b=b, how can you justify that? if a=b, then b=b, and b+b=2b. how can you explain that differently? how can you tell me that isnt true? is 1+1=1? no, 1+1=2(1). i fail to see where i am incorrect. yes, i followed your equation, but when you delcare a statement, you cant change it at will so it will apply to your formula. lets go sign a contract, but i will change it as i see fit. make sense? or course not.


by the way, the statement about stupidity applied to almost no one in this thread. most everyone has made a good point and proves the OP wrong.

thanks and have a great day

 

[gsellis]

Actually, the problem redefines the expression in midstream.

a - b = 0
(a + b) * (a - b) = b * (a - b)

The rule here is Anything multiplied by zero is zero.

So, the (a + b) * (a - b) = b * (a - b) equation has redefined the problem by taking two none related equivalent equations and applied the Multiple by Zero rule to both sides of the equation to make them equal. It is a misuse of multiple by zero.

So, the problem gets redefined as

a+b = b.

Therefore a = b = 0 is now the only solution.

 

[DrPizza]

Originally posted by: martind1

Originally posted by: martind1
hey i can prove

4 = 13


now follow this

(a-b) * (b-a^2) = (a^4 - 5) / (b^2*(a+1))


but you have to assume a= 4 or 6 when applicable and b = 29*pi^2 or 3


anything wrong with my math?

still holds true

I'd be hard to determine if anything is wrong with your math. Apparently, you're the only person on the planet doing "your" math. The other 5 or 6 billion of us use a different kind of math where the = sign means equality.

 

[MrDudeMan]

Originally posted by: gsellis
Actually, the problem redefines the expression in midstream.

a - b = 0
(a + b) * (a - b) = b * (a - b)

The rule here is Anything multiplied by zero is zero.

So, the (a + b) * (a - b) = b * (a - b) equation has redefined the problem by taking two none related equivalent equations and applied the Multiple by Zero rule to both sides of the equation to make them equal. It is a misuse of multiple by zero.

So, the problem gets redefined as

a+b = b.

Therefore a = b = 0 is now the only solution.

nice thinking...didnt even notice that! tack this onto our list of why this equation doesnt work

 

[MrDudeMan]

Originally posted by: DrPizza

Originally posted by: martind1

Originally posted by: martind1
hey i can prove

4 = 13


now follow this

(a-b) * (b-a^2) = (a^4 - 5) / (b^2*(a+1))


but you have to assume a= 4 or 6 when applicable and b = 29*pi^2 or 3


anything wrong with my math?

still holds true

I'd be hard to determine if anything is wrong with your math. Apparently, you're the only person on the planet doing "your" math. The other 5 or 6 billion of us use a different kind of math where the = sign means equality.

funniest quote of the day

 

[tmanndsu08]

If a-b=0 then a = b.

If a = b then 2b can't equal b. It's a contradiction.

If a-b almost equals 0 then a alsmost equals b.

If a almost equals b then 2b can't almost equal b.

Also, whenver you squar something you enter extrainious roots.w

 

[MrCodeDude]

Originally posted by: tmanndsu08
If a-b=0 then a = b.

If a = b then 2b can't equal b. It's a contradiction.

That's pretty much all you need to know.

 

[martind1]

in case noone has noticed by now, i was mocking the original "proof". most people have realized that this original proof holds no merit what soever. fewer have noticed that i was joking. not even i attempted my math, since i jsut made it up on the top of my head.


oh well. at least we werent debated wheter macs or pcs were better