2=1?

[ququ]

So I heard theres this formula to prove 2=1 and I seen it for a sec but then he took it away from me cuz he had to go and this was some random guy in a airport. Does anyone have this formula to show?

[techgnome]

OI! It's been a long time since I've done that... I'm not sure I remember how it all breaks down, but I know what formula you're talking about. It makes some assumptions: X = Y and X<> 0 ... when you break it all down and then make the appropriate replacements you end up with 2X = X ... divide both sides by X and you get 2 = 1

-tg

[techgnome]

And it's not a formula that proves it... it's an Algebraic expression that when reduced, shows that 2 = 1.

-tg

[ququ]

well when he showed it to me i seen a error with it so i wanted to see it again so see if i was right or not cuz i believe it is wrong

[stlaural]

I think you're looking for this (http://www.jimloy.com/algebra/two.htm).
EDIT : the trap is that it does not work because of a division by 0 if I'm not mistaken.

[ququ]

yes thank your that is exactly it that the fact u cant divide by zero so this hole formula is like a big myth right? correct me if im wrong but its how it looks to me

[stlaural]

That is also what I think unless someone can find a formula with no error.

[ququ]

Well Can any1 Find me a formula with no error?

[opus]

Who do you want, a formula showing that 1=2 with no errors?
You are gugu are what

[zaza]

You expect that somebody capable of proving that 2 actually does equal 1, thereby undermining the whole of mathematics and rendering our current scientific interpretation of the world completely meaningless would be hanging around on VB Forums answering questions like this?

[techgnome]

Hey.... according to Intel 0.9999999999999999999999999999999999 = 1 .... if they can redefine the rules of math, I don't see why we can't. At least we'll have our precision correct.

-tg

[jemidiah]

To be fair IEEE floating point arithmetic makes no attempt to exactly keep every property of arithmetic on a subset of the rationals intact. Associativity, for instance, doesn't hold.

zaza's of course right. If you could prove 2=1, you'd have 4=2+2=1+1=2=1, similarly 8=1, ..., 2^k=1 for any k>=1. Since every integer can be written in binary as a sum of powers of 2, you could show with strong induction that any number n is equal to 1, where n is a positive whole number. You also have 1 = 2-1 = 1-1 = 0, and 1 = 2-1 = 1-1 = 1-2 = -1. So, all integers are equal to 1. Rational numbers, those of form n/m for integers n and m, with m non-zero, can then easily be seen to be equal to 1/1 = 1. Real numbers, which can be defined as sequences of rational numbers, are then themselves all 1. At this point, there are a huge number of contradictions. One of the more obvious is that physical measurement can't be expressed in these numbers, since any measurement is equal to any other if you quantify it using these numbers.

Proving 1=2 would undermine more than our current scientific understanding. You couldn't count things meaningfully, for instance.


Almost every 1=2 "proof" I've seen reduces to a division by zero error. Some are more clever. One I've posted before using basic calculus is...

x = 1 + 1 + 1 ... {x times}
x * x = x + x + x ... {x times}
d/dx (x*x) = 2x = d/dx (x+x+x ... {x times}) = 1+1+1 ... {x times} = x
=> 2x = x
=> 2=1

[techgnome]

Woah....back off... clearly you need a system restore. Your humor file has been truncated and appears to no longer work. I'd try to explain it, but then it wouldn't be as funny.

-tg

[jemidiah]

Woah....back off... clearly you need a system restore. Your humor file has been truncated and appears to no longer work. I'd try to explain it, but then it wouldn't be as funny.

-tg

I had smiled inwardly, and now outwardly :).

[NickThissen]

I know a few like these...

a = b
a2 = ab
a2 - b2 = ab - b2
(a - b)(a + b) = (a - b)b
a + b = b

Since a = b, we have
b + b = b
or
2b = 1b
2 = 1.

Of course there is a simple 'trick' that makes this proof invalid, otherwise our understanding of mathematics would be really turned upside down :p

Another one proving 1 = -1:

1 = sqrt(1)
also, 1 = -1 * -1

So
1 = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = i2 = -1.


The only thing that is actually true is something that people always seem to think is false:
0.999... = 1.

Here, the ... means that an infinite number of 9's follow.
This statement is perfectly true. There is no rounding, 0.999... is exactly equal to 1. There is also no limits involved. 0.999... and 1 are the same number.

[jemidiah]

There is also no limits involved. 0.999... and 1 are the same number.

Real numbers, as I alluded to above, are usually thought of as sequences of rationals which get closer and closer to what you might think of as a point on the real number line. In this way real numbers can be made concrete in terms of the well-known properties of rationals (and, therefore, integers).

These sequences of rationals are infinitely long. Using the obvious translation of the notation "0.999..." and "1" in this context, they represent rational sequences

"0.999..." = {0.9, 0.99, 0.999, 0.9999, ...}
"1" = {1, 1, 1, 1, ...}

However, the differences between the two sequences, {0.1, 0.01, 0.001, 0.0001, ...}, clearly tend to zero. Intuitively, both sequences are heading towards the same point on the real number line, but they're taking different routes to get there. When the difference between two sequences of rationals like those above goes to zero, mathematicians call the two sequences "equivalent" inasmuch as they represent the same real number. (To be slightly more technical, a real number when viewed in this light is usually thought of as the set of all equivalent sequences of rationals. But ah well.) So, "0.999..." = "1".

Saying the difference between the sequences goes to zero implicitly takes the limit of term-by-term differences. So, using the usual interpretations, there in fact is a limit involved, though it's a bit hidden.