Begin with
-1 = -1
Rearrange,
(-1/1) = (1/-1)
Square-root both sides
sqrt(-1/1) = sqrt(1/-1)
Expand,
sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1)
Cross-multiply,
sqrt(-1) x sqrt(-1) = sqrt(1) x sqrt(1)
Since complex number i = sqrt(-1)
i x i = 1 x 1
i^2 = 1
Since i^2 = -1
-1 = 1
Divide both sides by 2,
-1/2 = 1/2
Add 1 1/2 to both sides,
1 1/2 - 1/2 = 1 1/2 + 1/2
1 = 2 (proved)
(Note that the proof above is only for recreational maths)
2007-03-21 22:06:47
·
answer #1
·
answered by ideaquest 7
·
0⤊
0⤋
1 does not equal 2.
If it were true that 1 = 2, the whole mathematical foundation would crumble. Everything we know about counting would be destroyed. We can create something from nothing (since, if
1 = 2, then 0 = 1; i.e. something from nothing). Not only that, but we can make any number equal any number. Wanna make 2 = 4? Then
1 = 2. Multiply both sides.
2 = 4.
Here is the false proof that 1 = 2:
Let x = 1 and y = 1.
Then
x = y. Multiply both sides by x,
x^2 = xy. Subtract y^2 both sides,
x^2 - y^2 = xy - y^2
Factor both sides.
(x - y)(x + y) = y(x - y)
Cancel the common factor (x - y) from both sides.
x + y = y
Resubstitute x = 1 and y = 1,
1 + 1 = 1
2 = 1
2007-03-22 04:04:23
·
answer #2
·
answered by Puggy 7
·
1⤊
0⤋
Depends on how precisely you define the numbers.
If you define 1 as anything from 0.001-1.999,
and 2 as anything from 1.001 - 2.999,
then for many data points, 1=2
;)
Also, more simply, one two equals two.
P.s. If you know "the answer", then you shouldn't ask, but with math, it is simply a matter of applying a set of clearly defined rules - and we get to make up the rules! This means that there are always infinite answers to any given question, limited only by our imagination and by the base ten training that we have ingrained from childhood.
2007-03-22 03:59:42
·
answer #3
·
answered by Loulabelle 4
·
0⤊
0⤋
True.
By definition,there exists a number 1 such that 1=2
now let 1=1
therefore 1=2.
QED
Mathematicians wouldnt care one bit if 1=2. You arent trying to figure out anything 'true' in mathematics but only what follows deductively from given assertions. You can start out assuming 1=2 if you like, doesnt matter. You wont figure out anything interesting, but whatever makes you happy.
2007-03-22 04:01:21
·
answer #4
·
answered by Anonymous
·
2⤊
0⤋
True if there is one whole with 2 parts then 1 would = 2
2007-03-22 04:00:34
·
answer #5
·
answered by Anonymous
·
1⤊
0⤋
The answer is False. There's a popular proof that shows this is true, but the proof is flawed. Here's the proof, where a and b are equal, non-zero quantities.
a = b
(multiply by a)
a² = ab
(subtract b²)
a² - b² = ab - b²
(factor)
(a â b)(a + b) = b(a â b)
(divide out (a - b))
a + b = b
(since a = b, you get)
2b = b
(divide by b)
2 = 1
This is flawed, because you cannot divide out the quantity (a - b). That quantity equals zero, and dividing by zero is undefined.
2007-03-22 04:05:23
·
answer #6
·
answered by Anonymous
·
1⤊
0⤋
There is way to show that 1=2:
Let's say that a=b, so...
Multiply by a: a^2 = ab
Subtract b^2: a^2 - b^2 = ab - b^2
Using the classic identity:
(a+b)(a - b) = b(a-b), so..
a+b = b
If a=1, then b=1 (a=b), so...
1+1=1 or 2=1
But....there IS a flaw. Can you find it?
2007-03-22 04:06:37
·
answer #7
·
answered by blighmaster 3
·
1⤊
0⤋
This, the simplest question in first grade of primary school, is one of the hardest to solve by mathematicians. I did read Russell's Principles of Mathematics, but I can't claim to have understood the whole of it. There are professional mathematicians posting here, and perhaps one of them can explain the truth of this to you (and to me),
The algebraic proofs will not withstand philosophical scrutiny.
2007-03-22 04:06:07
·
answer #8
·
answered by obelix 6
·
0⤊
0⤋
false 1 does not = 2
1 is .
2 is . .
. < . .
therefore
. cannot = . .
2007-03-22 03:59:42
·
answer #9
·
answered by Anonymous
·
0⤊
0⤋
Yes.
2007-03-22 03:58:32
·
answer #10
·
answered by McWalmart 3
·
0⤊
0⤋