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
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
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. The same happens here: (a+b)(a-b)=b(a-b) - as above. Dave
http://forum.allaboutcircuits.com/showthread.php?t=5434 http://forum.allaboutcircuits.com/showthread.php?t=3168&page=2 these might also come in handy
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
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.
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.
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
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.
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?
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.
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 adding 25/4 on both sides. 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.
you took the positive "possibility", which is clearly not possible.. so.. you have to take the -ve possibility which is infarct TRUE!
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.
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
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