السبت، 4 ديسمبر 2010

number zero secrets


lot of people know that divide by zero has no meaning  but they did not know why? so here in this article i will explain basic concepts about zero and i will try to show why divide by zero has no meaning.
we know 12 / 3 mean that we want to divide 12 to 3 parts then every part equal 4 so too 12/2 = 6 finally 12 / 1 = 12 it is look like we want to put 12 pens in one Packet then we will put all pens in the packet but can we put 12  pens in 0 packets ? it isn't logical because there is no packets to put pens in it so this is the reason for why  divide by zero has no meaning .

is 0/0 = 1 or not ?
lets consider this 3X = 15 then 3 x X = 3 x 5 then X = 5 yes this is right accordingly, 0 x 5 = 0 x 7 but 7 ≠ 5 this mean 0/0  ≠ 1 because if 0/0 = 1 then it should be 5 =7  this is error.Also we know 3 x = 12 equal  x = 12/3, 5 x = 25 equal X = 25/5 and 0 X= 0  equal x = 0/0 but we know multiply 0 by any number = 0 this means that every number can equal 0/0 so 0/0 has meaning but is undefined 
ex : 0 x X = 0 then X = 0/0 here x may equal 1 ,2 ,3 ,4 , any other number because if 0x 2= 0 then 2 = 0/0 and 3 x 0 =0 than 3= 0/0 and so on i cannot define x  = 2 or 4 or 5 or ................
now we know why 0/0 undefined , how ca we define it?
we use limits 
let  f(x) = ( x²- 4 ) / (x - 2) is undefined at x = 2 but lim ( x²- 4 ) / (x - 2) = 2 +2 = 4 then we define f(x) = 4 at x = 2

   

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