Ramneet Kaur
Said..
The DIVISION, of any REAL NUMBER, by ZERO ( 0 ) is said to be not Defined. why Any REAL NUMBER, except ZERO, when DIVIDED by ZERO, is UNDEFINED. This is the proof of that.
(1) Let us begin by dividing the number ( 10 ) by ( 10 ), the answer is (1). Now, let us divide the number ( 10 ) by ( 5 ), the answer is ( 2 ). Now, divide the number ( 10 ) by ( 2 ), the answer is ( 5 ). If you notice, as we continue to Divide ( 10 ) by decreasing numbers, our Answers/Quotients are getting larger respectively.
(2) Now, let us divide ( 10 ) by ( 1 ), the answer is (10 ). Divide ( 10 ) by ( 1/2 ), the answer is ( 20 )...
( 10 ) divided by ( 1/100 ), the answer is ( 1000 ). Finally, ( 10 )divided by ( 1/1,000,000) is (10,000,000 ). Notice that the quotient is rapidly increasing to a very large number as the divisor of ( 10 ) rapidly decreases towards ( 0 ).
(3) So we conclude, that ( 10 ) divided by ( 0 ) approaches an infinitely large number, a Number so Large, we can not define it. We then say, the answer to the problem, " ( 10 ) divided by ( 0 ) ", is UNDEFINED. We will now look at the graphical approach by graphing the function f(x) = 10/x. We will look at numbers ( X ) between ( 10 ) and ( 0 ), that is as ( X ) approaches
( 0 ) from the right, the Graph of f(x) tends towards positive Infinity. Please click on the image to the left.