Precalculus : Define a Field

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Define A Field

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

Possible Answers:

We have  for any  and  in the field.

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. 

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.

A field can be defined in many ways.

Correct answer:

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.

Explanation:

It is not the case that for any element  in a field, there is another one  such that their product is . Take  in the real numbers. Multiply  by any number and you get , so you will never get . This is true for any field that has more than 1 element.

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