∞ x 0 = -1 [?]

[p_2001]

any number x 2 is not equal to that number(except for 0 and infinity).For eg
a x 2 = a (That's not possible).You won't understand. This have given up trying.

understood the proof??


the fuck did I get a "-1" for posting this?

[parad0x]

x^2 + x = 0...
now, if according to you
we solve it
x(x+1) = 0... and now cross multiply "x"
we get
x+1 = 0
hence x = -1... getting it?

but, x can also be 0 ...
where did the other solution go?
it vanished when you decided to cross multiply...
whenever, wherever, you cross multiply ANYTHING, make a note that it is not 0.
in this case we lost a solution because of this.
THUS, you can never ever cross multiply 0's, it is wrong on too many levels.

For the answer to your question, the other solution went nowhere. You had given a quadratic equation and for any algebric equation, the number of roots are equal to its highest power(I forgot what is the term) on the variable.So it'll have 2 roots. Either you put -1 or 0, you'll get the answer 0.
BTW, what's your current status of knowledge? I mean to say what you are studying?

understood the proof??


the fuck did I get a "-1" for posting this?

I got "-2", for clearing the doubt of z3ro. I won't help anyone in future!

[p_2001]

For the answer to your question, the other solution went nowhere. You had given a quadratic equation and for any algebric equation, the number of roots are equal to its highest power(I forgot what is the term) on the variable.So it'll have 2 roots. Either you put -1 or 0, you'll get the answer 0.
BTW, what's your current status of knowledge? I mean to say what you are studying?

you got the proof for -1 right??
Do you know sandwich theorem?
en.m.wikipedia.org/wiki/Squeeze_theorem

as for the quadratic, true. Yes, while you can be certain that there are exactly two roots.
it was just used as an example.

what I meant was that whenever you bring something to denominator, you must mention that it cannot be a zero. Take this rule to heart.


and what I provided was a classic and simple example for why. While in this care you May know, there are higher order equations. and not just that, you will find that this is a very common mistake.


as for my edu.?
does it matter whether i'm an iitian or if I failed my class 12 math? as long as my proof is right?


I'm a 4th year student of computer science engineering.

 

[z3ro]

@ p_2001 : your math is good. I got it. Thanks! +1   

As for 'parad0x'... huh    Sorry.. but your math sucks... so does your attitude...

[Snayler]

I got "-2", for clearing the doubt of z3ro. I won't help anyone in future!

That must be because of your attitude:

Those rules doesn't apply on 0 and infinity, you idiot.

We're all civilized people, there's no need for insults.

[lucid]

Ok..

It's amazing to me that a simple topic about a math problem gets people mad enough to start throwing negative karma around.

Seriously. Calm down or I'm closing this.

[parad0x]

@z3ro: My maths is better than yours.
@p_2001: As you said in your proof

we can conclude that the X and Y axis must follow the same pattern

You have not prooved anything, you just gave an example to support your proof. There's absolutely no proof to prove infinity x 0 = -1.

[p_2001]

@z3ro: My maths is better than yours.
@p_2001: As you said in your proof You have not prooved anything, you just gave an example to support your proof. There's absolutely no proof to prove infinity x 0 = -1.

did you bother reading the sandwich theorem?

learn limits and their applications

[sudeep]

As much as I know, ∞ x 0 is an indeterminate form. There are in total 7 indeterminate forms viz. 0/0, ∞/∞, ∞x0, ∞-∞, 0^0, ∞^0, 1^∞
and these can be solved using Limits only.
@ p_2001 : I agree with you.

[bluechill]

*sigh* infinity * 0 may be equal to -1 it may not be.  It all depends on context.  Infinity * 0 is not always -1!

Case and point:

http://math.stackexchange.com/questions/28940/why-is-infinity-multiplied-by-zero-not-an-easy-zero-answer

In this case it may be but it is not always the case.  Hence why there is something called L'Hopitals rule for instance when taking derivatives.

[R3ckless]

Well.. you are implying you know the value of ∞..

[z3ro]

Well.. you are implying you know the value of ∞..

From what I understand.. infinity just a concept... not a number or something

[Mordred]

From what I understand.. infinity just a concept... not a number or something

That's correct. Also I didn't read all of the posts because I saw too much flaming, but if I may offer a solution to what the OP asked.

There is a theorem that says that the slopes of two perpendicular lines multiplied is equal to -1, indeed.

You are however interpreting the theorem incorrectly. It's okay to say that the product of two slopes for two lines that are perpendicular is -1, however you can't generalize it to ∞ x 0 = -1. Whilst that might be true in certain circumstances, it's a wrong interpretation of the theorem.

You have to operate in context, which means you have to operate with trig functions. Proof follows:

Assumption: Two lines, l1 and l2, are perpendicular to one another and have not special particularities. We want to know what is the value of the product of the two slopes for l1 and l2.

Proof: We take m1 to be the slope of l1 and m2 to be the slope of l2. The slope of a line is defined as being the tangent(A) where A is the angle that the line makes with the oX axis.

m1 = tan (A).

We know l1 and l2 are perpendicular, so we can extend l1 and l2 until they intersect the oX axis. We now have a triangle with a 90 degree angle at the intersection between l1 and l2. From the triangle definition, we can say:

angle l1 (A) + angle l2 (lets call it B) + 90 = 180
or
A + B = 90

We want to calculate m1 * m2 = tan (A) * tan (B). But A+B=90 => A = 90-B.
m1*m2 = tan(90-B) * tan(B) = -1/(tan B) * (tan B) = -1/(tan B) * (tan B) = -1. Q.E.D.

Maybe this is clear enough I hope.