



 
Hi Bill, The number 1 plays a special role in the arithmetic of the real numbers. For any real number a,
There are times when you have a real number and you somehow want to use this number to generate the number 1. For example you might ask
If such a number c exists we call it the reciprocal of b and write it b^{1} or sometimes 1/b. The difficulty that results is that if the number b that is given is actually 0 then we are asking "Given a real number 0 is there a real number c so that 0 × c = 1?" Clearly the answer is no since for any real number c, 0 × c = 0. Thus the number we might want to call the reciprocal of 0 and write 0^{1} or 1/0 doesn't exist. I hope this helps,  


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