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Why is 1 = 2 ??????

Originally posted by: paadness
No, i am not doing X-X to obtain Zero.

Ok beat this.

let,

(X-X) = A

now eq becomes

X(A)= (X+X)(A)

😀
Click to expand...

If (X-X) = A, then A must be zero, no matter what tricks you play with it, and dividing by A then implies division by zero and is undefined. At least if you're working with integers or real numbers. 'X(A) = (X+X)(A)' becomes '0*x = 0*(2*x)', otherwise known as '0 = 0'.

Thanks for playing.
 
but as far as i know, 0/0 can have 3 values.

Basically it involves limit and 0/0 is a dangerious thing. Le-Hopital rule has a solution to it if u have a denomitor.

In different situations we can treat this danger according to needs.

Still 1 = 2 trick is good enough to fool high school students 😛

 
De-Hopital's rule applies to a limit. There is no limit involved here. A does not approach 0, A is 0. Of course I could be wrong, but from what I understand from De-Hopital's rule, it doesn't apply here.
 
Originally posted by: paadness
but as far as i know, 0/0 can have 3 values.

Basically it involves limit and 0/0 is a dangerious thing. Le-Hopital rule has a solution to it if u have a denomitor.

In different situations we can treat this danger according to needs.

Still 1 = 2 trick is good enough to fool high school students 😛
Click to expand...

limit approaching zero isn't undefined. divide by zero is.

0/2 = 0, 0/1 = 0, 0/0 = undefined. No cheating 😛
 
L'Hopital's rule applies to LIMITS

0/0 = undefined. ALWAYS. 0/0 is undefined.

However, if evaluating something like
lim (as x -> 0) sin(x) / x
then, since the value is approaching 0 in the numerator and 0 in the denominator, which is an indeterminate form of a limit, THEN you can apply L'Hopital's rule. (in which case, it becomes lim (as x -> 0) cos(x) / 1 which would evaluate to 1/1 or 1.

Now, you said something about 3 values?
lim (as x -> 0) sinx / x = 1
lim (as x -> 0) sin2x / x = 2
lim (as x -> 0) sin3x / x = 3
lim (as x -> 0) sin4x / x = 4

obviously, we can come up with a limit problem, the answer to which can be any real number we want.
There are other limits of the form 0/0 which evaluate to:
There is no limit, it increases without bound. (usually just abbreviated as +infinity; the math people know what you mean)
There is no limit, it decreases without bound. (usually just abbreviated as -infinity; again, the math people know what you mean)
and
There is no limit because it approaches different values depending on the direction the limiting value is approached from (DNE)
 
Originally posted by: DrPizza
L'Hopital's rule applies to LIMITS

0/0 = undefined. ALWAYS. 0/0 is undefined.

However, if evaluating something like
lim (as x -> 0) sin(x) / x
then, since the value is approaching 0 in the numerator and 0 in the denominator, which is an indeterminate form of a limit, THEN you can apply L'Hopital's rule. (in which case, it becomes lim (as x -> 0) cos(x) / 1 which would evaluate to 1/1 or 1.

Now, you said something about 3 values?
lim (as x -> 0) sinx / x = 1
lim (as x -> 0) sin2x / x = 2
lim (as x -> 0) sin3x / x = 3
lim (as x -> 0) sin4x / x = 4

obviously, we can come up with a limit problem, the answer to which can be any real number we want.
There are other limits of the form 0/0 which evaluate to:
There is no limit, it increases without bound. (usually just abbreviated as +infinity; the math people know what you mean)
There is no limit, it decreases without bound. (usually just abbreviated as -infinity; again, the math people know what you mean)
and
There is no limit because it approaches different values depending on the direction the limiting value is approached from (DNE)
Click to expand...

:thumbsup:
 
Originally posted by: krcat1
Originally posted by: jman19
Originally posted by: krcat1
X(X-X) does not equal X2-X2 if you set (X-X) = A

X(A) = (X+X)(A) unless A=0
Click to expand...

X(A) = (X+X)(A) even if A=0...
Click to expand...

X(A) = (X+X)(A) only if A=0
Click to expand...

For some reason when I decided to reply I completely ignored the fact that A is set to (X-X). Anyway, "only if" doesn't ever pertain, as that IS the value of A.
 
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