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

[Samirat]

I'm just saying, this is actually how you notate negative multiplication. Your problem is that you can't actually visualize a negative number? That's true. It's very hard to subtract something that doesn't already exist. The only way to really conceptualize negative numbers is in their positive opposites. For instance, to visualize subtracting 4, you have to have 4 things to take away.

Yes, I know.. thats what I was trying to do with having 4, -4s to start off with.

I'm not entirely sure what you mean with the "half" thing. Half of a cake is still half of a cake, even if you see it as a whole. It's like if you take half of 4. It's a whole 2. But it's still half of 4.

With regard to the only ever seeing 'wholes', its quite an interesting theoretical concept; we as humans cannot actually create half of something in the real world; it is a purely abstract idea that is taken for granted by most (and by me until I read about it in a book a while back... maybe by Roger Penrose?). Note how you had to have recourse to numbers?

I like how this threads now gone completely off-topic now... and seems to be about the visualisation of abstract mathematical concepts.

Nothing wrong with numbers. I still don't see why halves aren't valid. If you have 4 equal tomatoes, and halve that, you could get 2 tomatoes, 4 halves of tomatoes, or 4 tomatoes of half their previous density, but all of these are half of what you had before (Assuming by half you meant half mass). While these are still whole objects, and we see them as such, they're still half what you had before, and we can see them as that as well. We can't see half as an abstract quantity, but it doesn't actually exist as an abstract quantity.

 

[Lukeje]

Nothing wrong with numbers. I still don't see why halves aren't valid. If you have 4 equal tomatoes, and halve that, you could get 2 tomatoes, 4 halves of tomatoes, or 4 tomatoes of half their previous density, but all of these are half of what you had before (Assuming by half you meant half mass). While these are still whole objects, and we see them as such, they're still half what you had before, and we can see them as that as well. We can't see half as an abstract quantity, but it doesn't actually exist as an abstract quantity.

Yes, but whatever real world examples you say, I will always see the entirety of that partial quantity.

 

[Samirat]

Nothing wrong with numbers. I still don't see why halves aren't valid. If you have 4 equal tomatoes, and halve that, you could get 2 tomatoes, 4 halves of tomatoes, or 4 tomatoes of half their previous density, but all of these are half of what you had before (Assuming by half you meant half mass). While these are still whole objects, and we see them as such, they're still half what you had before, and we can see them as that as well. We can't see half as an abstract quantity, but it doesn't actually exist as an abstract quantity.

Yes, but whatever real world examples you say, I will always see the entirety of that partial quantity.

Yes, but while you see the whole of the half, so to speak, you can also see the half of the whole. The half of the whole pie and the whole of the half pie are one and the same. It's just a slight difference in perspective, between seeing what's not there and what is there. Those that see the glass as half empty see half of the whole.

 

[Lukeje]

Yes, but while you see the whole of the half, so to speak, you can also see the half of the whole. The half of the whole pie and the whole of the half pie are one and the same. It's just a slight difference in perspective, between seeing what's not there and what is there. Those that see the glass as half empty see half of the whole.

To see half of something, you actually have the whole of it there to compare, otherwise 'half' is just a concept in your mind. You have to go through the rationalisation of remembering what a whole one was, and then comparing. But in the real world, it is still an entire 'thing'.

 

[The Blue Mongoose]

6. Divide through by x:
2 = 1

here is where you mess up.

should bring both xs to one side.

2x = 1x
> 1x = 0
> x = 0

YOU WIN THE INTERNET!

so you did divide by zero... you just called zero x

wait... 2/0... oh Fu-!

 

[Syntax Error]

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.