Proof: 1 = 2 (no division by zero!)

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I wonder if someone in these boards would be likely to prove that i exists, and show it in the number line.

 

[crepesack]

you did your divide 2x=1x wrong dude,what you did is impossible, however I can prove .999repeating =1 easily ill show you REAL math not fakeness
two ways to do this...

8/9=.888..
9/9=.999 & 1 it has to be

then a more complicated algebraic proof
let x represent .9repeating
so we can say
x=.9...
therefore
10x=9.9...
10x-x=9.9...-x
9x=9
x=1
:.
x=.9... and 1
flawless algebra so easy a first grader could do it

edit:to all those who dont think .999... times 10 is 9.999repeating go back to school

 

[breadlord]

function

NOW it makes more sense.

Since I'm in high school, my head almost exploded, but it didn't.


OMG major bump.

 

[wrecker77]

*Bangs head on glass*

I was never good at math! This just makes me feel bad....

Wait if 1=2...I was right all along. Now if you will excuse me, I have a 8th grader math teacher to call. Take that Mr.Heinsen I am smart!

 

[Jaythulhu]

Here's one just to bake your noodles and annoy the mathgeeks amongst us a little more

Theorem: All numbers are equal.
Proof: Choose arbitrary a and b, and let t = a + b. Then
a + b = t
(a + b)(a - b) = t(a - b)
a^2 - b^2 = ta - tb
a^2 - ta = b^2 - tb
a^2 - ta + (t^2)/4 = b^2 - tb + (t^2)/4
(a - t/2)^2 = (b - t/2)^2
a - t/2 = b - t/2
a = b
So all numbers are the same, and math is pointless.

 

[Sporky111]

This was done just a couple months ago. Even 20 pages later, people still couldn't agree. 1 doesn't equal 2. It's an error in your math.

(1+1+1. . .)x can't be condensed because 1x + 1x . . . doesn't equal x

 

[tsb247]

I LOVE math threads. I think we need more of them - They are fun!

 

[Iron Mal]

Now I'm not very good at maths but I'm pretty certain that one and two are very much seperate numbers and are not interchangable.

Sure, you can probably create an equation that suggests that under certain conditions and if calculated in a certain way then they have an equal value but let's not get ahead of ourselves here.

When will we realistically use this knowledge? (I believe this is one of the main reasons that many people dread maths in school, the teacher is often quite content to drone on about formulas and equations that serve no useful purpose to man or beast, in essence, they wasted time that I could have used chatting up the girls in my class).

 

[Seldon2639]

The problem is with the derivative. the expansion is fine, but by the chain rule you have an extra factor of x you didn't account for; that handwaved in 'x times' is still a function of x.

That's kind of what I saw. The derivative of the right side (when removing the hand-wavy-ness) ends up as:

dx/dx (x)x = x . OP, you fall into the fallacy most supposed "proofs" of mathematical impossibilities do: you try to use english approximations of mathematical values. The issue is that it's impossible. English is too varied a language to allow for true translation; there's too much equivocation (which you do).

Think of it this way, to draw an analogy.

Nothing is better than sex
Masturbation is better than nothing
Therefore, masturbation is better than sex.

Nothing in this sense is used not only to indicate a null set, but to also indicate absolute zero. See the problem?

 

[randomsix]

4. As these are the same equation, their derivative must be the same. Take the derivative of both sides:
d(x^2)/dx = d((x + x + x + ...) x times)/dx
2x = (1 + 1 + 1 + ...) x times.

You are telling lies.

d((x*x)/dx = x+x by the product rule.

That sum of yours isn't a standalone function, it's the result of a function.

What you did there was take the derivative your sum incorrectly.

Marbas is right. You're bastardizing x² into a line of slope x at whatever point you are testing and then comparing that to the derivative of x². It comes out different because you mistakenly changed the equation into something else.

 

[Seldon2639]

5. Condense the right side:
2x = x

6. Divide through by x:
2 = 1

I stripped out everything except for the two really bad steps. Five is the one that's the tip off for your proof being wrong.

There are only three ways for 2x to be equal to x.

1. Give up the identity property of X. Thus x =/= x. It solves step five, but makes step six impossible.
2. Give up the identity property of the real numbers (it does happen in some higher level math). It solves step five, and step six, but doesn't allow for your conclusion to make any sense, since your proof can no longer support the proposition that 1 = 1, or that 2 = 2.
3. Have x = 0 or infinity.

Ignoring any of the steps it took to get you to 2x = x (and there are other earlier errors) that's the most staggering. There is no number for x (assuming constant values for 1 and 2) which can yield a true response to 2x = x. It can't happen using standard math.

My best guess is that you're dropping the identity property of x, since you do mess with it in step four, but that would make it impossible to divide both sides by x as a way to remove it.

4. As these are the same equation, their derivative must be the same. Take the derivative of both sides:
d(x^2)/dx = d((x + x + x + ...) x times)/dx
2x = (1 + 1 + 1 + ...) x times.

This is the other big time issue I see. Even ignoring that dx/dx wouldn't actually yield a derivative in any real way (since you'd be taking the change in x over the change in x, which wouldn't offer any derivative other than one), you don't properly derive the right side.

You can't make x*x into discrete terms simply by dividing them with words. Your method would be akin to saying that dy/dx of X^2 is the same as X(X) or x times x. Since the derivative of x = 1, the derivative of x^2 is 1, since 1(1) is 1. Even if your logic worked, you forget to derive both parts of the right side. You don't derive the "x times" portion itself, which would yield (following your logic) 2x = (1 + 1 + 1 + ...) 1 time. Either derive fully, or not at all.

 

[FallenJellyDoughnut]

One is the loneliest number that you'll ever do
Two can be as bad as one, its the loneliest number since the number one
No is the saddest experience you'll ever know
Yes is the saddest experience you'll ever know
cause one is the loneliest number that you'll ever know
one is the loneliest number even worst then two
yeah!

 

[dududf]

http://www.youtube.com/watch?v=H91rPIq2mN4

That vid pretty much sums up what just happend in my head.