∞ x 0 = -1 [?]

[z3ro]

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 ?   

                                     

∞ x 0 = -1

[parad0x]

So you want to ask why,right?

[z3ro]

euhh..      yeahh..
But.. is that right?      ∞ x 0 = -1

[parad0x]

euhh..      yeahh..
But.. is that right?      ∞ 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.

[p_2001]

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?

[parad0x]

@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.

[z3ro]

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.

  You mad???!
1/0 =∞,
=> 2/0 = ∞,
=> 3/0 = ∞

Then what? 1 = 2 =3 ?
 

If

 a/b = z  &
 c/b = z

a = c      you can't just cross-multiply.

[parad0x]

  You mad???!
1/0 =∞,
=> 2/0 = ∞,
=> 3/0 = ∞

Then what? 1 = 2 =3 ?
 

If

 a/b = z  &
 c/b = z

a = c      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.

[z3ro]

a/b cannot equal to a.Are you understanding what am I talking about?

Why? If b = 1 ?  ahhahaa

0/5= 0 &
0/7=0.
That doesn't mean 5 = 7.

  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 

[parad0x]

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.

[z3ro]

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...

[parad0x]

From what I understand.. infinity is.. a concept.. not a value.. right?   

Yeah, infinity is something what you can't define. Is is undefined.

[z3ro]

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   
 

[p_2001]

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?


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.

[parad0x]

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.