Precalculus : Define a Field

Study concepts, example questions & explanations for Precalculus

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Real Numbers

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

Possible Answers:

A field can be defined in many ways.

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

We have  for any  and  in the 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.

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.

Learning Tools by Varsity Tutors