real number?

Question

for each a, there exist a unique real number 1/a.
*explain why this is not true.

Answer 1

To expand on that, there is no value for 1/0 because you cannot mathematically answer the question, "How many zeros are there in one?" There is a kind of answer, that of "infinity", but that is not a real number. Therefore, a cannot equal zero.

Zero is, of course, a real number, because it can be located on a number line, and it can designate a position in space.

Answer 2

1/0 does not exist, therefore, a cannot = zero.

Answer 3

1. a is not constrained to be non-zero
2. a is not constrained to be real. The reciprocal of a complex number is a complex number.