EvilZone
Encyclopedia Galactica => Science => : z3ro January 27, 2013, 02:18:31 PM
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The product of the gradient of any two perpendicular lines is -1. Right?
So... the product of ∞ (gradient of y-axis) and 0 (gradient of x-axis) is equal to -1 ? :o
∞ x 0 = -1
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So you want to ask why,right?
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euhh.. ??? yeahh..
But.. is that right? :o ∞ x 0 = -1
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euhh.. ??? yeahh..
But.. is that right? :o ∞ x 0 = -1
That's right.
Proof: 1/0 =∞ , right
=> 2/0 = ∞,
=> 3/0 = ∞,
Therefore anything divided by 0 = ∞ (except 0/0 which is an indeterminent form.)
=> -1/0 = ∞.
On cross multiplying,we get
∞ x 0 = -1.
Hence, prooved. ;)
My maths teacher also asked my the same when teaching us the properties of straight lines.I also gave him the same answer and his face was like a pumpkin. lol
Hope you understood it. :)
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Eh... In simpler math it will be difficult to explain.
first of all, slope of 'y' is undefined and hence, cannot be talked about.
@perfect, your proof is incorrect. You cannot cross multiply.
there exists a proof through trigonometry.
but, the question is whether you know compound angle formula? for tan(x+y)?
And, do you understand limits?
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@perfect, your proof is incorrect. You cannot cross multiply.
Why can't I cross multiply and I know about compound angle formula.
I am not saying to cross multiplying, I am saying that take 0 to other side. You can't solve 0 x infinity.
tan(x + y) = (tan x + tan y)/(1 - tan x * tan y)
I want to see how you'll prove this using that formula?
I also understand limits.
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That's right.
Proof: 1/0 =∞ , right
=> 2/0 = ∞,
=> 3/0 = ∞,
Therefore anything divided by 0 = ∞ (except 0/0 which is an indeterminent form.)
=> -1/0 = ∞.
On cross multiplying,we get
∞ x 0 = -1.
Hence, prooved. ;)
:o You mad???!
1/0 =∞,
=> 2/0 = ∞,
=> 3/0 = ∞
Then what? 1 = 2 =3 ?
::)
If
a/b = z &
c/b = z
a = c 8) you can't just cross-multiply.
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:o You mad???!
1/0 =∞,
=> 2/0 = ∞,
=> 3/0 = ∞
Then what? 1 = 2 =3 ?
::)
If
a/b = z &
c/b = z
a = c 8) you can't just cross-multiply.
Those rules doesn't apply on 0 and infinity, you idiot. >:(
For example,
a/b cannot equal to a. But if you put a = 0, a/b = a.
Are you understanding what am I talking about?
0/5= 0 &
0/7=0.
That doesn't mean 5 = 7.
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a/b cannot equal to a.Are you understanding what am I talking about?
Why? If b = 1 ? :P :P ahhahaa
0/5= 0 &
0/7=0.
That doesn't mean 5 = 7.
:o you got it all wrong dude... I never said it that way....
if
a/b = z &
c/b = z
a = c = bz
You got you denominator and numerator the wrong way around ::)
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Why can't you understand that general rules don't apply on 0 and infinity. >:(
For the denominator as 1.There can be some exceptions.
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From what I understand.. infinity is.. a concept.. not a value.. right? ???
Why can't you understand that general rules don't apply on 0 and infinity
yeah.. maybe.. :-\ but still...
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From what I understand.. infinity is.. a concept.. not a value.. right? ???
Yeah, infinity is something what you can't define. Is is undefined.
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Something else just crossed my disturbed mind ~ ~ ~
Consider, ∞ x 2
Basically, this implies 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + ...
addind 2 to 2 an infinite number of times...
conclusion: ∞ x 2 = ∞
Ok?
similarly, ∞ x 0
0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 +...
No way you're going to get -1
???
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Why can't I cross multiply and I know about compound angle formula.
I am not saying to cross multiplying, I am saying that take 0 to other side. You can't solve 0 x infinity.
tan(x + y) = (tan x + tan y)/(1 - tan x * tan y)
I want to see how you'll prove this using that formula?
I also understand limits.
@p_2001: Why can't I cross multiply and I know about compound angle formula.
tan(x + y) = (tan x + tan y)/(1 - tan x * tan y)
I want to see how you'll prove this using that formula?
you never ever cross multiply 0 anywhere....
there is no such thing as "cross multiplication"
what actually happens is
Eg.
a = b ........
a* 1/b = b* 1/b ( multiplying both sides by 1/b , or rather dividing both sides by b)
now, can you really say you divided both sides by 0? :D
another example..
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.
now, coming to the PROOF
slope of any linear equation or rather a straight line = tan(X) = m.
now, let us assume a line with angle (90 + h) where h tends to 0. This line will intersect
the Y axis at infinity.
a line perpendicular to this will be one making angle " h " with the x axis.
our goal, find tan h * tan990+h)
now, slope = tan(90+h) = tan( h+90) = [tan h + tan 90] / [1 - tan h tan 90]
divide and multiply by tan(90).
------>>>> [tanh/tan90 +1] / [ 1/tan90 - tanh]
thus [0+1] / [0- tan h] (since 1/tan 90 = 0)
thus,
tan (90+h) * tan (h) = -1...
similarly, now you can find tan ( 90 -h ) and tan (-h)..
and it will again come as -1.
thus, we can say that line 90 + h and line 90-h both sandwich the Y axis and their perpendiculars will sandwich the x axis.
now, since tan ( 90 +h) * tan (h) = -1 and the same goes for 90-h, we can conclude that the X and Y axis must follow the same pattern since the three line are almost
concident and parallel and intersect at infinity.
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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.
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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?
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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! >:(
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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.
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@ p_2001 : your math is good. I got it. Thanks! +1 ;)
As for 'parad0x'... huh ::) Sorry.. but your math sucks... so does your attitude...
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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.
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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.
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@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.
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@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
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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.
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*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.
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Well.. you are implying you know the value of ∞..
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Well.. you are implying you know the value of ∞..
From what I understand.. infinity just a concept... not a number or something
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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.