Test: Precalculus

1.

Which of the following is not true about a field. (Note: the real numbers  is a field)

For every element  in the field, there is another element  such that their product   is equal to , where  is the multiplicative identity,  in the case of real numbers.

There is an element  in the field such that  for any element  in the field.

For every element  in the field, there is another element  such that their sum  is equal to , where  is the additive identity. 

A field can be defined in many ways.

We have  for any  and  in the field.

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