I am a college student and have been asked to explain and figure out why we can't
divide by zero. this is an elementary question that was posed by one of my
professors. My e-mail address is email@example.com I really appreciate
any feedback that I can get. thank you,
Illinois State University
I wouldn't be as categorical as to say that you can't divide by zero. You CAN divide by zero, you just don't get a real number as the result. You get something with some unusual properties.
Suppose that 1/0=J then, since 2*0=0, J+J=1/0 + 1/0 = 1/(2*0) + 1/(2*0) = 1/2 (J+J) = J, so J+J=J. Also J*J=(1/0)*(1/0) = (1*1)/(0*0) = 1/0 = J. Thus J*J=2*J=J. This mathematical object, J, we usually call infinity. The correct statement is that 1/0 is not a real number.
There are however some things to be wary of; for example 0/0, 0*J and J - J. In these cases you need more information; in fact, Newton and Leibniz invented calculus to be able to solve such problems.
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