# Strange Mathematics

#### Dave

Joined Nov 17, 2003
6,969
Here's one:

Say: x = y

Then: x - y = 0

And: 2x - 2y = 0

So: x - y = 2x - 2y

Taking common factors: 1(x - y) = 2(x - y)

Therefore: 1 = 2 !!!

(I know this is not really the answer, but it certainly confuses many who see it!)

Dave

#### recca02

Joined Apr 2, 2007
1,212
divison by zero is meaningless
indeterminate,
incorrect,
forbidden,
u have invoked the wrath of the math deity for those who r confused
since X-Y =0
division by it is not allowed in the factor part.,under the section @#@#\$ of the math act.
this is a punishable offense .

similar thing in a different way
warning if u are below 8 years of mental age the below proof will give u mental torture.
a=b
a^2=b^2
a^2=a.b
a^2-b^2=ab-b^2
(a+b)(a-b)=b(a-b)
a+b=b
2b=b
2=1

#### Dave

Joined Nov 17, 2003
6,969
divison by zero is meaningless
indeterminate,
incorrect,
forbidden,
u have invoked the wrath of the math deity for those who r confused
since X-Y =0
Indeed that is the issue, but the unsuspecting will miss that point and assume that it is mathematical magic! You can also see that since x - y = 0, then 1(x - y) = 2(x - y) equates to 0 = 0, and not 1 = 2.

a=b
a^2=b^2
a^2=a.b
a^2-b^2=ab-b^2
(a+b)(a-b)=b(a-b)
a+b=b
2b=b
2=1
The same happens here: (a+b)(a-b)=b(a-b) - as above.

Dave

#### Dave

Joined Nov 17, 2003
6,969

#### recca02

Joined Apr 2, 2007
1,212
Oh yeah, remember them. I think this shows that the problem is down to interpretation of the question...and the subsequent lack of understanding!

Dave considering i was the one to raise the incorrect diffrentiation question #### Dave

Joined Nov 17, 2003
6,969 considering i was the one to raise the incorrect diffrentiation question D'oh! I meant in general of course... Dave

#### recca02

Joined Apr 2, 2007
1,212
D'oh! I meant in general of course... Dave
well i know it wasnt meant for me since my maths skills are exceptional
i know 5 + 8 = 14 when it comes to maths there is more to it than just some proofs;

consider this graph which can not be plotted;
plot y Vs x

Y = 1 : for x = rational number;
Y = -1 : for x = irrational number.

_______
4 out of 3 ppl have trouble with fractions.

#### Dave

Joined Nov 17, 2003
6,969
well i know it wasnt meant for me since my maths skills are exceptional
i know 5 + 8 = 14 Very good! when it comes to maths there is more to it than just some proofs;

consider this graph which can not be plotted;
plot y Vs x

Y = 1 : for x = rational number;
Y = -1 : for x = irrational number.
Go on then, explain.

Dave

#### recca02

Joined Apr 2, 2007
1,212
well its an example that proves not all functions can be plotted,
since there are infinite irrational numbers between two rational numbers and vice versa, between the two smallest points there are infinite points not even the best super computer (thats me ) can plot it.

#### Dave

Joined Nov 17, 2003
6,969
since there are infinite rational numbers between two rational numbers and vice versa, between the two smallest points there are infinite point
You mean irrational here  Ok, I get it now. I thought you were suggesting plotting Y = 1 : for x = rational number and Y = -1 : for x = irrational number seperately, hence my confusion.

Dave

#### gbm46

Joined May 6, 2007
47
random aside:

Consider a staircase with 5 steps. The height of the staircase is 1m and the width also 1. So the the total width plus height of the stairs must be 1 + 1. Now visualise 100 steps - still 2m for total width/height. At infinitety steps the stair case will resemble a straight line, so the length is root2?

I also think Ive seen a mathematical paradox based on this. It had something to do with a half circle with an infinite number of smaller half circles cut out of it on its straight edge, and eventually proved that pi = 2.

This also relates somehow to Feynman diagrams but I don't know what they are yet.

#### recca02

Joined Apr 2, 2007
1,212
i m a bit confused since i m not confused by the staircase example,
i mean root2 wud be the length of ladder taken from starting pt to end point and the perimeter length wud be 1+1 ,i fail to see the paradox.
i want to have a look at the pi=2 proof ,can u post it?

#### n9352527

Joined Oct 14, 2005
1,198
It does resemble a straight line, but it is not. As the number of steps approaches infinity, the height and width of the steps would approach zero. The total height and width would still be the sum of all steps' heights and widths.

#### recca02

Joined Apr 2, 2007
1,212
i need some explanation to this,
i know where the error lies but a flawless explanation of it is what i cud not give to my friend so plz do so for me.

-6=-6
4-10=9-15
4-10+25/4=9-15+25/4
now (a-b)^2=a2 +b2 -2ab
so
(2-5/2)^2=(3-5/2)^2
so taking sq rt
2-5/2=3-5/2
2=3 ??????????
i understand while taking sq rt we must consider both +ve and -ve roots.
but when i think abt the +ve sign possiblity i get a little confused abt how to explain.
care to explain a bit?

nevermind i got it.
have fun getting confused.

#### ajay_bhargav

Joined May 9, 2007
5
you took the positive "possibility", which is clearly not possible.. so.. you have to take the -ve possibility which is infarct TRUE!

#### recca02

Joined Apr 2, 2007
1,212
ok maybe i shud explain what got me confused,
we generally solve for root fo x in a equation/equality and get two roots which wud suffice as an answer ,
the rarity of this senseless proof posted above is u solve without a variable and compare two roots instead of comparing a variable with a root.

#### ajay_bhargav

Joined May 9, 2007
5
aha.. correct.. so thats the reason.. the possibility you think, can be true is actually not true #### xenotime

Joined Nov 10, 2007
5
i want to have a look at the pi=2 proof ,can u post it?
It origins from the Buffon's needle problem. You can use this
theorem to calculate the value of pi using statistical methods by throwing
some needles (toothpicks) on a ruled paper.

The formula used is pi = 2(total no. of throws)/no. of cuts

No. of throws means the total number of needles thrown (like 10
needles thrown 100 times = 1000).

Cuts = needles landing with an intersection with any line.

Distance between parallel lines = length of the needle.

Solution:

Let the needles have length L1 and the parallel lines be drawn a
distance L2 (L2 >= L1) apart. A 'success' occurs when any part of a
needle cuts a line.

We can think of the centre of the needle being uniformly distributed
between 0 and L2/2. Let the smaller of the angles between the
direction of a needle and the parallel lines be theta, so that theta
is uniformly distributed between 0 and pi/2.

If y is the distance of mid-point of the needle from the closest line,
then we get an intersection if:

y < (L1/2)sin(theta)

We now draw two axes with y up the vertical axis varying from 0 to
L2/2, and theta along the horizontal axis varying from 0 to pi/2.
The sample space is any point within this rectangular area =
(pi/2)(L2/2). If you draw the curve

y = (L1/2)sin(theta)

from 0 to pi/2, then the area under this curve divided by the total
area of the rectangle will give the probability of an intersection.

The area under the sine curve is INT[(L1/2)sin(theta)]

= -(L1/2)cos(theta) from 0 to pi/2

= -L1/2[0 - 1] = L1/2

Probability of an intersection = (L1/2)/(pi/2)(L/2)

Probability = (2L1)/(pi.L2)

Also Probability = (No.of cuts)/(No.of throws) = (2L1)/(pi.L2)

From this pi= (2L1.Number of throws)/(L2.Number of cuts)

So, for L1 = L2, pi=2 #### steeve_wai

Joined Sep 13, 2007
47
you have divided both sides by x-y=0.division by zero is "illegal".why?
consider p/0 = q; p and q are non-zero.
we have p=0*q.say p=10
no value of q when multiplied with 0 will give you 10.
please comment,if you feel that there are faults with my posts or if i can improve my explanations...thank you